diff --git a/src/flake8/violation.py b/src/flake8/violation.py
index 8535178..c9c240e 100644
--- a/src/flake8/violation.py
+++ b/src/flake8/violation.py
@@ -2,8 +2,10 @@
 from __future__ import annotations
 
 import functools
+import io
 import linecache
 import logging
+import tokenize
 from re import Match
 from typing import NamedTuple
 
@@ -16,7 +18,20 @@ LOG = logging.getLogger(__name__)
 
 @functools.lru_cache(maxsize=512)
 def _find_noqa(physical_line: str) -> Match[str] | None:
-    return defaults.NOQA_INLINE_REGEXP.search(physical_line)
+    comment_tokens = []
+    try:
+        tokens = tokenize.generate_tokens(io.StringIO(physical_line).readline)
+        for token in tokens:
+            if token.type == tokenize.COMMENT:
+                comment_tokens.append(token.string)
+    except tokenize.TokenError:
+        pass
+
+    for comment in comment_tokens:
+        match = defaults.NOQA_INLINE_REGEXP.search(comment)
+        if match is not None:
+            return match
+    return None
 
 
 class Violation(NamedTuple):
diff --git a/tests/integration/test_main.py b/tests/integration/test_main.py
index 0ca5b63..e5ac7d4 100644
--- a/tests/integration/test_main.py
+++ b/tests/integration/test_main.py
@@ -259,6 +259,25 @@ x = """
     assert out == err == ""
 
 
+def test_noqa_in_string_is_not_ignored(tmpdir, capsys):
+    """See https://github.com/pycqa/flake8/issues/1321."""
+    t_py_src = '''\
+def f():
+    x = '# noqa'
+'''
+
+    with tmpdir.as_cwd():
+        tmpdir.join("t.py").write(t_py_src)
+        assert cli.main(["t.py"]) == 1
+
+    expected = """\
+t.py:2:5: F841 local variable 'x' is assigned to but never used
+"""
+    out, err = capsys.readouterr()
+    assert out == expected
+    assert err == ""
+
+
 def test_physical_line_file_not_ending_in_newline(tmpdir, capsys):
     """See https://github.com/PyCQA/pycodestyle/issues/960."""
     t_py_src = "def f():\n\tpass"
diff --git a/tests/unit/test_violation.py b/tests/unit/test_violation.py
index 1b4852b..b5f1dfd 100644
--- a/tests/unit/test_violation.py
+++ b/tests/unit/test_violation.py
@@ -28,6 +28,7 @@ from flake8.violation import Violation
         ("E111", "a = 1  # noqa - We do not care", True),
         ("E111", "a = 1  # noqa: We do not care", True),
         ("E111", "a = 1  # noqa:We do not care", True),
+        ("E111", "a = '# noqa'", False),
         ("ABC123", "a = 1  # noqa: ABC123", True),
         ("E111", "a = 1  # noqa: ABC123", False),
         ("ABC123", "a = 1  # noqa: ABC124", False),