diff --git a/CHANGES b/CHANGES
index a71f25aaa5c..2cec105d868 100644
--- a/CHANGES
+++ b/CHANGES
@@ -23,6 +23,7 @@ Features added
 * #8588: autodoc: :confval:`autodoc_type_aliases` now supports dotted name. It
   allows you to define an alias for a class with module name like
   ``foo.bar.BazClass``
+* #9175: autodoc: Special member is not documented in the module
 * #3257: autosummary: Support instance attributes for classes
 * #9129: html search: Show search summaries when html_copy_source = False
 * #9120: html theme: Eliminate prompt characters of code-block from copyable
diff --git a/sphinx/ext/autodoc/__init__.py b/sphinx/ext/autodoc/__init__.py
index ff6475c9442..fa0b6af74c5 100644
--- a/sphinx/ext/autodoc/__init__.py
+++ b/sphinx/ext/autodoc/__init__.py
@@ -709,6 +709,8 @@ def is_filtered_inherited_member(name: str, obj: Any) -> bool:
             # if isattr is True, the member is documented as an attribute
             if member is INSTANCEATTR:
                 isattr = True
+            elif (namespace, membername) in attr_docs:
+                isattr = True
             else:
                 isattr = False
 
@@ -769,7 +771,6 @@ def is_filtered_inherited_member(name: str, obj: Any) -> bool:
                 else:
                     # keep documented attributes
                     keep = True
-                isattr = True
             elif want_all and isprivate:
                 if has_doc or self.options.undoc_members:
                     if self.options.private_members is None:
diff --git a/tests/roots/test-ext-autodoc/target/module.py b/tests/roots/test-ext-autodoc/target/module.py
new file mode 100644
index 00000000000..fe3b490a92d
--- /dev/null
+++ b/tests/roots/test-ext-autodoc/target/module.py
@@ -0,0 +1,14 @@
+undocumented = 1
+
+#: docstring
+documented = 1
+
+undoc_annotated: int
+
+#: docstring
+annotated: int
+
+__special__ = 1
+
+#: docstring
+__documented_special__ = 1
diff --git a/tests/test_ext_autodoc_automodule.py b/tests/test_ext_autodoc_automodule.py
index 3332704bbe6..59296a981a3 100644
--- a/tests/test_ext_autodoc_automodule.py
+++ b/tests/test_ext_autodoc_automodule.py
@@ -29,6 +29,95 @@ def test_empty_all(app):
     ]
 
 
+@pytest.mark.sphinx('html', testroot='ext-autodoc')
+def test_automodule(app):
+    options = {'members': None}
+    actual = do_autodoc(app, 'module', 'target.module', options)
+    assert list(actual) == [
+        '',
+        '.. py:module:: target.module',
+        '',
+        '',
+        '.. py:data:: annotated',
+        '   :module: target.module',
+        '   :type: int',
+        '',
+        '   docstring',
+        '',
+        '',
+        '.. py:data:: documented',
+        '   :module: target.module',
+        '   :value: 1',
+        '',
+        '   docstring',
+        '',
+    ]
+
+
+@pytest.mark.sphinx('html', testroot='ext-autodoc')
+def test_automodule_undoc_members(app):
+    options = {'members': None,
+               'undoc-members': None}
+    actual = do_autodoc(app, 'module', 'target.module', options)
+    assert list(actual) == [
+        '',
+        '.. py:module:: target.module',
+        '',
+        '',
+        '.. py:data:: annotated',
+        '   :module: target.module',
+        '   :type: int',
+        '',
+        '   docstring',
+        '',
+        '',
+        '.. py:data:: documented',
+        '   :module: target.module',
+        '   :value: 1',
+        '',
+        '   docstring',
+        '',
+        '',
+        '.. py:data:: undoc_annotated',
+        '   :module: target.module',
+        '   :type: int',
+        '',
+    ]
+
+
+@pytest.mark.sphinx('html', testroot='ext-autodoc')
+def test_automodule_special_members(app):
+    options = {'members': None,
+               'special-members': None}
+    actual = do_autodoc(app, 'module', 'target.module', options)
+    assert list(actual) == [
+        '',
+        '.. py:module:: target.module',
+        '',
+        '',
+        '.. py:data:: __documented_special__',
+        '   :module: target.module',
+        '   :value: 1',
+        '',
+        '   docstring',
+        '',
+        '',
+        '.. py:data:: annotated',
+        '   :module: target.module',
+        '   :type: int',
+        '',
+        '   docstring',
+        '',
+        '',
+        '.. py:data:: documented',
+        '   :module: target.module',
+        '   :value: 1',
+        '',
+        '   docstring',
+        '',
+    ]
+
+
 @pytest.mark.sphinx('html', testroot='ext-autodoc',
                     confoverrides={'autodoc_mock_imports': ['missing_module',
                                                             'missing_package1',