diff --git a/CHANGES b/CHANGES
index 85a4f9def..b22e05b8f 100644
--- a/CHANGES
+++ b/CHANGES
@@ -16,6 +16,7 @@ Features added
 Bugs fixed
 ----------
 
+* #7839: autosummary: cannot handle umlauts in function names
 * #7715: LaTeX: ``numfig_secnum_depth > 1`` leads to wrong figure links
 
 Testing
diff --git a/sphinx/ext/autosummary/__init__.py b/sphinx/ext/autosummary/__init__.py
index 162b6868c..7eaefd4b1 100644
--- a/sphinx/ext/autosummary/__init__.py
+++ b/sphinx/ext/autosummary/__init__.py
@@ -755,7 +755,8 @@ def process_generate_options(app: Sphinx) -> None:
     with mock(app.config.autosummary_mock_imports):
         generate_autosummary_docs(genfiles, suffix=suffix, base_path=app.srcdir,
                                   app=app, imported_members=imported_members,
-                                  overwrite=app.config.autosummary_generate_overwrite)
+                                  overwrite=app.config.autosummary_generate_overwrite,
+                                  encoding=app.config.source_encoding)
 
 
 def setup(app: Sphinx) -> Dict[str, Any]:
diff --git a/sphinx/ext/autosummary/generate.py b/sphinx/ext/autosummary/generate.py
index fe7daf214..7583d9894 100644
--- a/sphinx/ext/autosummary/generate.py
+++ b/sphinx/ext/autosummary/generate.py
@@ -347,7 +347,7 @@ def generate_autosummary_docs(sources: List[str], output_dir: str = None,
                               info: Callable = None, base_path: str = None,
                               builder: Builder = None, template_dir: str = None,
                               imported_members: bool = False, app: Any = None,
-                              overwrite: bool = True) -> None:
+                              overwrite: bool = True, encoding: str = 'utf-8') -> None:
     if info:
         warnings.warn('info argument for generate_autosummary_docs() is deprecated.',
                       RemovedInSphinx40Warning, stacklevel=2)
@@ -415,17 +415,17 @@ def generate_autosummary_docs(sources: List[str], output_dir: str = None,
 
         filename = os.path.join(path, name + suffix)
         if os.path.isfile(filename):
-            with open(filename) as f:
+            with open(filename, encoding=encoding) as f:
                 old_content = f.read()
 
             if content == old_content:
                 continue
             elif overwrite:  # content has changed
-                with open(filename, 'w') as f:
+                with open(filename, 'w', encoding=encoding) as f:
                     f.write(content)
                 new_files.append(filename)
         else:
-            with open(filename, 'w') as f:
+            with open(filename, 'w', encoding=encoding) as f:
                 f.write(content)
             new_files.append(filename)