diff --git a/starlette/staticfiles.py b/starlette/staticfiles.py
index 8822efd10..3af22a824 100644
--- a/starlette/staticfiles.py
+++ b/starlette/staticfiles.py
@@ -153,7 +153,7 @@ async def lookup_path(
             try:
                 stat_result = await aio_stat(full_path)
                 return (full_path, stat_result)
-            except FileNotFoundError:
+            except (FileNotFoundError, NotADirectoryError):
                 pass
         return ("", None)
 
diff --git a/tests/test_staticfiles.py b/tests/test_staticfiles.py
index da1c250a8..e4220cde0 100644
--- a/tests/test_staticfiles.py
+++ b/tests/test_staticfiles.py
@@ -243,3 +243,15 @@ def test_staticfiles_html(tmpdir):
     response = client.get("/missing")
     assert response.status_code == 404
     assert response.text == "<h1>Custom not found page</h1>"
+
+
+def test_staticfiles_access_file_as_directory(tmpdir):
+    path = os.path.join(tmpdir, "example.txt")
+    with open(path, "w") as file:
+        file.write("<file content>")
+
+    app = StaticFiles(directory=tmpdir)
+    client = TestClient(app)
+    response = client.get("/example.txt/foo")
+    assert response.status_code == 404
+    assert response.text == "Not Found"