diff --git a/sphinx/ext/napoleon/docstring.py b/sphinx/ext/napoleon/docstring.py
index 6c866f3db42..3c33eca92b2 100644
--- a/sphinx/ext/napoleon/docstring.py
+++ b/sphinx/ext/napoleon/docstring.py
@@ -358,7 +358,7 @@ def __init__(
         self._what: _AutodocObjType | Literal['object'] = what
         self._name = name
         self._obj = obj
-        if options:
+        if options is not None:
             try:
                 self._no_index = options.no_index or options.noindex
             except (AttributeError, TypeError):
diff --git a/tests/test_ext_autodoc/test_ext_autodoc.py b/tests/test_ext_autodoc/test_ext_autodoc.py
index 0d2c29d13fb..8f526e051cf 100644
--- a/tests/test_ext_autodoc/test_ext_autodoc.py
+++ b/tests/test_ext_autodoc/test_ext_autodoc.py
@@ -2639,11 +2639,7 @@ def test_singledispatchmethod_classmethod_automethod() -> None:
     ]
 
 
-@pytest.mark.skipif(
-    sys.version_info[:2] >= (3, 13),
-    reason='Cython does not support Python 3.13 yet.',
-)
-@pytest.mark.skipif(pyximport is None, reason='cython is not installed')
+@pytest.mark.skipif(pyximport is None, reason='Cython is not installed')
 def test_cython() -> None:
     options = {
         'members': None,