diff --git a/src/flake8/utils.py b/src/flake8/utils.py
index 29df9bc..e0c221a 100644
--- a/src/flake8/utils.py
+++ b/src/flake8/utils.py
@@ -448,7 +448,7 @@ def matches_filename(path, patterns, log_message, logger):
     if not patterns:
         return False
     basename = os.path.basename(path)
-    if fnmatch(basename, patterns):
+    if basename not in {".", ".."} and fnmatch(basename, patterns):
         logger.debug(log_message, {"path": basename, "whether": ""})
         return True
 
diff --git a/tests/unit/test_utils.py b/tests/unit/test_utils.py
index 803d643..c84a03b 100644
--- a/tests/unit/test_utils.py
+++ b/tests/unit/test_utils.py
@@ -1,4 +1,5 @@
 """Tests for flake8's utils module."""
+import logging
 import os
 
 import mock
@@ -296,3 +297,10 @@ MULTI_FILE_INFO = {
 def test_parse_unified_diff(diff, parsed_diff):
     """Verify that what we parse from a diff matches expectations."""
     assert utils.parse_unified_diff(diff) == parsed_diff
+
+
+def test_matches_filename_for_excluding_dotfiles():
+    """Verify that `.` and `..` are not matched by `.*`."""
+    logger = logging.Logger(__name__)
+    assert not utils.matches_filename('.', ('.*',), '', logger)
+    assert not utils.matches_filename('..', ('.*',), '', logger)