diff --git a/news/changelog-1.11.md b/news/changelog-1.11.md
index 4944dc36ba8..9f5bba7c53e 100644
--- a/news/changelog-1.11.md
+++ b/news/changelog-1.11.md
@@ -45,6 +45,7 @@ All changes included in 1.11:
 ### `pdf`
 
 - ([#14982](https://github.com/quarto-dev/quarto-cli/issues/14982)): Fix a footnote in document metadata, such as `title` or `author`, making PDF and Typst output shift heading levels, which turned the first level-1 heading into the document title.
+- ([#15027](https://github.com/quarto-dev/quarto-cli/issues/15027)): Fix PDF rendering with regional German variants such as `lang: de-CH` failing when German hyphenation patterns are not installed, instead of installing them automatically.
 
 ### `revealjs`
 
diff --git a/src/command/render/latexmk/parse-error.ts b/src/command/render/latexmk/parse-error.ts
index 2b760243231..a9c1588b0c0 100644
--- a/src/command/render/latexmk/parse-error.ts
+++ b/src/command/render/latexmk/parse-error.ts
@@ -156,36 +156,115 @@ export function findPdfAccessibilityWarnings(
   return result;
 }
 
-// Finds missing hyphenation files (these appear as warnings in the log file)
-export function findMissingHyphenationFiles(logText: string) {
-  //ngerman gets special cased
-  const filterLang = (lang: string) => {
-    // It seems some languages have no hyphenation files, so we just filter them out
-    // e.g. `lang: zh` has no hyphenation files
-    // https://github.com/quarto-dev/quarto-cli/issues/10291
-    const noHyphen = ["chinese-hans", "chinese"];
-    if (noHyphen.includes(lang)) {
-      return;
-    }
+// Hyphenation pattern names (in language.dat) whose package is not
+// hyphen-<name>, according to `execute AddHyphen` in texlive.tlpdb
+const kHyphenationPackageNames: Record<string, string> = {
+  ngerman: "german",
+  swissgerman: "german",
+  pinyin: "chinese",
+  ukenglish: "english",
+  british: "english",
+  usenglishmax: "english",
+  bokmal: "norwegian",
+  norsk: "norwegian",
+  nynorsk: "norwegian",
+  schoolfinnish: "finnish",
+  monogreek: "greek",
+  ibycus: "ancientgreek",
+  classiclatin: "latin",
+  liturgicallatin: "latin",
+  mongolianlmc: "mongolian",
+  serbianc: "serbian",
+  // older names (synonyms in texlive.tlpdb)
+  amharic: "ethiopic",
+  geez: "ethiopic",
+  persian: "farsi",
+  patois: "french",
+  francais: "french",
+  polygreek: "greek",
+  portuges: "portuguese",
+  slovene: "slovenian",
+  espanol: "spanish",
+  // all of these are in the hyphen-indic package
+  assamese: "indic",
+  bengali: "indic",
+  gujarati: "indic",
+  hindi: "indic",
+  kannada: "indic",
+  malayalam: "indic",
+  marathi: "indic",
+  oriya: "indic",
+  pali: "indic",
+  panjabi: "indic",
+  tamil: "indic",
+  telugu: "indic",
+};
+
+// Maps a babel language name to the TeX Live package providing its
+// hyphenation patterns (undefined when there is no such package)
+function hyphenationPackageForLanguage(lang: string) {
+  // Names in language.dat may be in mixed case (e.g. UKenglish)
+  lang = lang.toLowerCase();
+
+  // It seems some languages have no hyphenation files, so we just filter them out
+  // e.g. `lang: zh` has no hyphenation files
+  // https://github.com/quarto-dev/quarto-cli/issues/10291
+  const noHyphen = ["chinese-hans", "chinese"];
+  if (noHyphen.includes(lang)) {
+    return;
+  }
+
+  // NOTE Although the names of the corresponding lfd files match those in this list,
+  // there are some exceptions, particularly in German and Serbian. So, ngerman is
+  // called here german, which is the name in the CLDR and, actually, the most logical.
+  //
+  // See https://ctan.math.utah.edu/ctan/tex-archive/macros/latex/required/babel/base/babel.pdf
+  const name = Object.hasOwn(kHyphenationPackageNames, lang)
+    ? kHyphenationPackageNames[lang]
+    : lang;
+  const pkg = `hyphen-${name}`;
+  // The name comes from the log and is passed to tlmgr (through a .bat file
+  // on Windows), so only keep what looks like a package name (all
+  // hyphenation names in texlive.tlpdb are lowercase letters, digits and hyphens)
+  if (/^hyphen-[a-z0-9-]+$/.test(pkg)) {
+    return pkg;
+  }
+}
 
-    // NOTE Although the names of the corresponding lfd files match those in this list,
-    // there are some exceptions, particularly in German and Serbian. So, ngerman is
-    // called here german, which is the name in the CLDR and, actually, the most logical.
-    //
-    // See https://ctan.math.utah.edu/ctan/tex-archive/macros/latex/required/babel/base/babel.pdf
-    if (lang === "ngerman") {
-      return "hyphen-german";
+// babel raises a fatal error (rather than the warning handled by
+// findMissingHyphenationFiles) when a language is referenced but has neither
+// hyphenation patterns in the format nor a dialect fallback. For instance,
+// babel-german checks `\iflanguage{ngerman}` at begin document, which fails for
+// `lang: de-CH` or `lang: de-AT` when hyphen-german is not installed:
+//   ! Package babel Error: You haven't defined the language 'ngerman' yet.
+// https://github.com/rstudio/tinytex/issues/515
+// Older babel versions use `ngerman' or no quotes at all.
+const kBabelUndefinedLanguageRegex =
+  /Package babel Error: You haven't defined the language [`']?([^`'\s]+)[`']? yet/g;
+
+// Finds hyphenation packages whose absence makes the compilation fail
+// (to be installed directly by name, as opposed to the file search terms
+// returned by findMissingFontsAndPackages)
+export function findMissingHyphenationPackages(logText: string): string[] {
+  const packages: string[] = [];
+  for (const match of logText.matchAll(kBabelUndefinedLanguageRegex)) {
+    const pkg = hyphenationPackageForLanguage(match[1]);
+    if (pkg) {
+      packages.push(pkg);
     }
-    return `hyphen-${lang.toLowerCase()}`;
-  };
+  }
+  return ld.uniq(packages);
+}
 
+// Finds missing hyphenation files (these appear as warnings in the log file)
+export function findMissingHyphenationFiles(logText: string) {
   const babelWarningRegex = /^Package babel Warning:/m;
   const hasWarning = logText.match(babelWarningRegex);
   if (hasWarning) {
     const languageRegex = /^\(babel\).* language [`'](\S+)[`'].*$/m;
     const languageMatch = logText.match(languageRegex);
     if (languageMatch) {
-      return filterLang(languageMatch[1]);
+      return hyphenationPackageForLanguage(languageMatch[1]);
     }
   }
 
@@ -196,7 +275,7 @@ export function findMissingHyphenationFiles(logText: string) {
   if (match) {
     const language = match[1];
     if (language) {
-      return filterLang(language);
+      return hyphenationPackageForLanguage(language);
     }
   }
 }
diff --git a/src/command/render/latexmk/pdf.ts b/src/command/render/latexmk/pdf.ts
index 2e7d5010de2..756906d21e3 100644
--- a/src/command/render/latexmk/pdf.ts
+++ b/src/command/render/latexmk/pdf.ts
@@ -21,6 +21,7 @@ import {
   findLatexError,
   findMissingFontsAndPackages,
   findMissingHyphenationFiles,
+  findMissingHyphenationPackages,
   findPdfAccessibilityWarnings,
   kMissingFontLog,
   needsRecompilation,
@@ -28,6 +29,7 @@ import {
 import { error, info, warning } from "../../../deno_ral/log.ts";
 import { logProgress } from "../../../core/log.ts";
 import { isWindows } from "../../../deno_ral/platform.ts";
+import * as ld from "../../../core/lodash.ts";
 
 export async function generatePdf(mkOptions: LatexmkOptions): Promise<string> {
   if (!mkOptions.quiet) {
@@ -470,8 +472,15 @@ async function findAndInstallPackages(
     const logText = Deno.readTextFileSync(logFile);
 
     const searchTerms = findMissingFontsAndPackages(logText, dirname(logFile));
-    if (searchTerms.length > 0) {
-      const packages = await pkgMgr.searchPackages(searchTerms);
+    // Packages known by name (no tlmgr file search needed)
+    const namedPackages = findMissingHyphenationPackages(logText);
+    if (searchTerms.length > 0 || namedPackages.length > 0) {
+      const packages = ld.uniq([
+        ...namedPackages,
+        ...(searchTerms.length > 0
+          ? await pkgMgr.searchPackages(searchTerms)
+          : []),
+      ]);
       if (packages.length > 0) {
         const packagesInstalled = await pkgMgr.installPackages(
           packages,
diff --git a/tests/docs/smoke-all/2026/10/12/15027.qmd b/tests/docs/smoke-all/2026/10/12/15027.qmd
new file mode 100644
index 00000000000..9ca84f6fa5e
--- /dev/null
+++ b/tests/docs/smoke-all/2026/10/12/15027.qmd
@@ -0,0 +1,28 @@
+---
+title: "Swiss German hyphenation auto-install (#15027)"
+format: pdf
+lang: de-CH
+_quarto:
+  tests:
+    pdf: null
+---
+
+**Only remove packages on CI**
+
+```{r}
+#| eval: !expr isTRUE(as.logical(Sys.getenv("CI", "false")))
+#| include: false
+#| messages: "NA"
+
+# Remove the German babel and hyphenation packages to test auto-installation.
+# Without hyphen-german, babel fails with a fatal error for `lang: de-CH`:
+# "You haven't defined the language 'ngerman' yet."
+for (pkg in c("hyphen-german", "babel-german")) {
+  if (tinytex::check_installed(pkg)) {
+    message("Removing '", pkg, "' package for the render")
+    tinytex::tlmgr_remove(pkg)
+  }
+}
+```
+
+Dieses Dokument prüft, dass Quarto `babel-german` und `hyphen-german` automatisch installiert, wenn `lang: de-CH` verwendet wird (siehe auch rstudio/tinytex#515).
diff --git a/tests/unit/latexmk/parse-error.test.ts b/tests/unit/latexmk/parse-error.test.ts
index 2410e00a66b..0c991a0b56c 100644
--- a/tests/unit/latexmk/parse-error.test.ts
+++ b/tests/unit/latexmk/parse-error.test.ts
@@ -5,9 +5,9 @@
 *
 */
 
-import { findLatexError, findMissingFontsAndPackages, findMissingHyphenationFiles } from "../../../src/command/render/latexmk/parse-error.ts"
+import { findLatexError, findMissingFontsAndPackages, findMissingHyphenationFiles, findMissingHyphenationPackages } from "../../../src/command/render/latexmk/parse-error.ts"
 import { unitTest } from "../../test.ts";
-import { assert } from "testing/asserts";
+import { assert, assertEquals } from "testing/asserts";
 
 function fontSearchTerm(font: string): string {
   const fontPattern = font.replace(/\s+/g, '\\s*');
@@ -163,4 +163,176 @@ unitTest("Detect missing hyphenation with babel warnings", async () => {
   );
 }, {
   cwd: () => "unit/latexmk/"
-})
\ No newline at end of file
+})
+
+unitTest("Detect missing hyphenation causing a fatal babel error", async () => {
+  // `lang: de-CH` without hyphen-german (https://github.com/rstudio/tinytex/issues/515):
+  // babel-german defines nswissgerman as a dialect of the null language, but then
+  // checks `\iflanguage{ngerman}`, which is a fatal error, so compilation fails.
+  const logSwissGerman = `Package babel Warning: No hyphenation patterns were preloaded for
+(babel)                the language 'German (current orthography), needed by Swiss Standard German (current orthography)' into the format.
+(babel)                Please, configure your TeX system to add them and
+(babel)                rebuild the format. Now I will use the patterns
+(babel)                preloaded for \\language=0 instead on input line 1260.
+
+Package babel Info: Hyphen rules for 'nswissgerman' set to \\l@nil
+(babel)             (\\language5). Reported on input line 1260.
+
+! Package babel Error: You haven't defined the language 'ngerman' yet.
+(babel)                Perhaps you misspelled it or your installation
+(babel)                is not complete.
+
+See the babel package documentation for explanation.
+Type  H <return>  for immediate help.`;
+  assertEquals(
+    findMissingHyphenationPackages(logSwissGerman),
+    ["hyphen-german"],
+    "Should map the undefined ngerman language to hyphen-german",
+  );
+  // The file-based search finds nothing for this error
+  assertEquals(findMissingFontsAndPackages(logSwissGerman, "."), []);
+
+  // Backtick-quote format (older babel)
+  assertEquals(
+    findMissingHyphenationPackages(
+      "! Package babel Error: You haven't defined the language `ngerman' yet.",
+    ),
+    ["hyphen-german"],
+  );
+  // Unquoted format (older babel)
+  assertEquals(
+    findMissingHyphenationPackages(
+      "! Package babel Error: You haven't defined the language ngerman yet.",
+    ),
+    ["hyphen-german"],
+  );
+  // Other languages are lowercased and prefixed
+  assertEquals(
+    findMissingHyphenationPackages(
+      "! Package babel Error: You haven't defined the language 'Spanish' yet.",
+    ),
+    ["hyphen-spanish"],
+  );
+  // Languages without hyphenation package are ignored
+  assertEquals(
+    findMissingHyphenationPackages(
+      "! Package babel Error: You haven't defined the language 'chinese-hans' yet.",
+    ),
+    [],
+  );
+  // Only the fatal error is considered, not babel warnings
+  assertEquals(
+    findMissingHyphenationPackages(`Package babel Warning: No hyphenation patterns were preloaded for
+(babel)                the language 'Spanish' into the format.`),
+    [],
+  );
+  assertEquals(findMissingHyphenationPackages("asdf qwer"), []);
+}, {
+  cwd: () => "unit/latexmk/"
+})
+
+unitTest("Drop hyphenation package names that are not valid package names", async () => {
+  // Language names come from the log and end up as tlmgr arguments, which
+  // go through a .bat file on Windows
+  for (const lang of ['x"&calc', "ngerman;id", "%PATH%", "a|b", "a^b", "--repository=x"]) {
+    assertEquals(
+      findMissingHyphenationPackages(
+        `! Package babel Error: You haven't defined the language '${lang}' yet.`,
+      ),
+      [],
+      `Should drop '${lang}' from the babel error`,
+    );
+    assertEquals(
+      findMissingHyphenationFiles(`Package babel Warning: No hyphenation patterns were preloaded for
+(babel)                the language '${lang}' into the format.`),
+      undefined,
+      `Should drop '${lang}' from the babel warning`,
+    );
+  }
+  // Valid names are kept
+  assertEquals(
+    findMissingHyphenationPackages(
+      `! Package babel Error: You haven't defined the language 'x"&calc' yet.
+! Package babel Error: You haven't defined the language 'french' yet.`,
+    ),
+    ["hyphen-french"],
+  );
+}, {
+  cwd: () => "unit/latexmk/"
+})
+
+unitTest("Map hyphenation language names to their TeX Live package", async () => {
+  // Names whose package is not hyphen-<name>, according to
+  // `execute AddHyphen` (name= and synonyms=) in texlive.tlpdb
+  const expected: Record<string, string> = {
+    ngerman: "hyphen-german",
+    swissgerman: "hyphen-german",
+    pinyin: "hyphen-chinese",
+    ukenglish: "hyphen-english",
+    british: "hyphen-english",
+    usenglishmax: "hyphen-english",
+    bokmal: "hyphen-norwegian",
+    norsk: "hyphen-norwegian",
+    nynorsk: "hyphen-norwegian",
+    schoolfinnish: "hyphen-finnish",
+    monogreek: "hyphen-greek",
+    polygreek: "hyphen-greek",
+    ibycus: "hyphen-ancientgreek",
+    classiclatin: "hyphen-latin",
+    liturgicallatin: "hyphen-latin",
+    mongolianlmc: "hyphen-mongolian",
+    serbianc: "hyphen-serbian",
+    amharic: "hyphen-ethiopic",
+    geez: "hyphen-ethiopic",
+    persian: "hyphen-farsi",
+    patois: "hyphen-french",
+    francais: "hyphen-french",
+    portuges: "hyphen-portuguese",
+    slovene: "hyphen-slovenian",
+    espanol: "hyphen-spanish",
+    assamese: "hyphen-indic",
+    bengali: "hyphen-indic",
+    gujarati: "hyphen-indic",
+    hindi: "hyphen-indic",
+    kannada: "hyphen-indic",
+    malayalam: "hyphen-indic",
+    marathi: "hyphen-indic",
+    oriya: "hyphen-indic",
+    pali: "hyphen-indic",
+    panjabi: "hyphen-indic",
+    tamil: "hyphen-indic",
+    telugu: "hyphen-indic",
+  };
+  for (const [lang, pkg] of Object.entries(expected)) {
+    assertEquals(
+      findMissingHyphenationPackages(
+        `! Package babel Error: You haven't defined the language '${lang}' yet.`,
+      ),
+      [pkg],
+      `Should map '${lang}' to ${pkg} from the babel error`,
+    );
+    assertEquals(
+      findMissingHyphenationFiles(`Package babel Warning: No hyphenation patterns were preloaded for
+(babel)                the language '${lang}' into the format.`),
+      pkg,
+      `Should map '${lang}' to ${pkg} from the babel warning`,
+    );
+  }
+  // Names in language.dat may be in mixed case
+  assertEquals(
+    findMissingHyphenationPackages(
+      "! Package babel Error: You haven't defined the language 'UKenglish' yet.",
+    ),
+    ["hyphen-english"],
+  );
+  // Several languages from the same package are installed once
+  assertEquals(
+    findMissingHyphenationPackages(
+      `! Package babel Error: You haven't defined the language 'hindi' yet.
+! Package babel Error: You haven't defined the language 'tamil' yet.`,
+    ),
+    ["hyphen-indic"],
+  );
+}, {
+  cwd: () => "unit/latexmk/"
+})