diff --git a/sphinx/ext/autosummary/__init__.py b/sphinx/ext/autosummary/__init__.py
index ece16c15b..350604387 100644
--- a/sphinx/ext/autosummary/__init__.py
+++ b/sphinx/ext/autosummary/__init__.py
@@ -252,7 +252,9 @@ class Autosummary(SphinxDirective):
             tree_prefix = self.options['toctree'].strip()
             docnames = []
             excluded = Matcher(self.config.exclude_patterns)
+            filename_map = self.config.autosummary_filename_map
             for name, sig, summary, real_name in items:
+                real_name = filename_map.get(real_name, real_name)
                 docname = posixpath.join(tree_prefix, real_name)
                 docname = posixpath.normpath(posixpath.join(dirname, docname))
                 if docname not in self.env.found_docs:
@@ -785,11 +787,11 @@ def setup(app: Sphinx) -> Dict[str, Any]:
     app.add_role('autolink', AutoLink())
     app.connect('builder-inited', process_generate_options)
     app.add_config_value('autosummary_context', {}, True)
+    app.add_config_value('autosummary_filename_map', {}, 'html')
     app.add_config_value('autosummary_generate', [], True, [bool])
     app.add_config_value('autosummary_generate_overwrite', True, False)
     app.add_config_value('autosummary_mock_imports',
                          lambda config: config.autodoc_mock_imports, 'env')
     app.add_config_value('autosummary_imported_members', [], False, [bool])
-    app.add_config_value('autosummary_filename_map', {}, 'html')
 
     return {'version': sphinx.__display_version__, 'parallel_read_safe': True}
diff --git a/sphinx/ext/autosummary/generate.py b/sphinx/ext/autosummary/generate.py
index 4454e47fc..98e2a047a 100644
--- a/sphinx/ext/autosummary/generate.py
+++ b/sphinx/ext/autosummary/generate.py
@@ -396,9 +396,6 @@ def generate_autosummary_docs(sources: List[str], output_dir: str = None,
 
     if app:
         filename_map = app.config.autosummary_filename_map
-        if not isinstance(filename_map, Mapping):
-            raise TypeError('autosummary_filename_map should be a mapping from '
-                            'strings to strings')
     else:
         filename_map = {}
 
diff --git a/tests/roots/test-ext-autosummary-filename-map/index.rst b/tests/roots/test-ext-autosummary-filename-map/index.rst
index ef27d9d19..e85389395 100644
--- a/tests/roots/test-ext-autosummary-filename-map/index.rst
+++ b/tests/roots/test-ext-autosummary-filename-map/index.rst
@@ -9,6 +9,5 @@
 
    autosummary_dummy_module
    autosummary_dummy_module.Foo
-   autosummary_dummy_module.Foo.Bar
+   autosummary_dummy_module.Foo.bar
    autosummary_dummy_module.bar
-   autosummary_dummy_module.qux
diff --git a/tests/test_ext_autosummary.py b/tests/test_ext_autosummary.py
index 62fe4cc56..462a93954 100644
--- a/tests/test_ext_autosummary.py
+++ b/tests/test_ext_autosummary.py
@@ -396,6 +396,9 @@ def test_autosummary_filename_map(app, status, warning):
     assert not (app.srcdir / 'generated' / 'autosummary_dummy_module.bar.rst').exists()
     assert (app.srcdir / 'generated' / 'autosummary_dummy_module.Foo.rst').exists()
 
+    html_warnings = app._warning.getvalue()
+    assert html_warnings == ''
+
 
 @pytest.mark.sphinx('latex', **default_kw)
 def test_autosummary_latex_table_colspec(app, status, warning):