diff --git a/Doc/whatsnew/3.13.rst b/Doc/whatsnew/3.13.rst
index 59b9281e6d2b89..e0490027c1e763 100644
--- a/Doc/whatsnew/3.13.rst
+++ b/Doc/whatsnew/3.13.rst
@@ -568,6 +568,12 @@ Deprecated
 * Deprecate undocumented :func:`!pydoc.ispackage` function.
   (Contributed by Zackery Spytz in :gh:`64020`.)
 
+* Deprecate the ``undefined`` codec. This codec always raises a
+  :exc:`ValueError` exception when being used. It was intended for use by the
+  :mod:`site` module to switch off automatic string to Unicode coercion, but
+  it's no longer used by the :mod:`site` module.
+  (Contributed by Victor Stinner in :gh:`76637`.)
+
 
 Pending Removal in Python 3.14
 ------------------------------
@@ -721,6 +727,12 @@ Pending Removal in Python 3.15
   All arguments will be removed from :func:`threading.RLock` in Python 3.15.
   (Contributed by Nikita Sobolev in :gh:`102029`.)
 
+* The codec ``undefined`` is deprecated. This codec always raises a
+  :exc:`ValueError` exception when being used. It was intended for use by the
+  :mod:`site` module to switch off automatic string to Unicode coercion, but
+  it's no longer used by the :mod:`site` module.
+  (Contributed by Victor Stinner in :gh:`76637`.)
+
 Pending Removal in Python 3.16
 ------------------------------
 
diff --git a/Lib/encodings/undefined.py b/Lib/encodings/undefined.py
index 4690288355c710..f40675fbeb82e6 100644
--- a/Lib/encodings/undefined.py
+++ b/Lib/encodings/undefined.py
@@ -10,6 +10,11 @@
 
 """
 import codecs
+import warnings
+
+
+warnings._deprecated('codec "undefined"', remove=(3, 15))
+
 
 ### Codec APIs
 
diff --git a/Lib/test/test_codecs.py b/Lib/test/test_codecs.py
index ff511a625a0194..e4b0421a51d329 100644
--- a/Lib/test/test_codecs.py
+++ b/Lib/test/test_codecs.py
@@ -1,12 +1,13 @@
 import codecs
 import contextlib
 import copy
+import encodings
 import io
 import locale
 import pickle
 import sys
 import unittest
-import encodings
+import warnings
 from unittest import mock
 
 from test import support
@@ -1744,6 +1745,11 @@ def test_open(self):
                 self.assertIsInstance(file, codecs.StreamReaderWriter)
 
     def test_undefined(self):
+        # ignore the DeprecationWarning
+        with warnings.catch_warnings():
+            warnings.simplefilter('ignore', category=DeprecationWarning)
+            codecs.lookup('undefined')
+
         self.assertRaises(UnicodeError, codecs.encode, 'abc', 'undefined')
         self.assertRaises(UnicodeError, codecs.decode, b'abc', 'undefined')
         self.assertRaises(UnicodeError, codecs.encode, '', 'undefined')
diff --git a/Misc/NEWS.d/next/Library/2024-01-08-23-55-50.gh-issue-76637.U9fXWx.rst b/Misc/NEWS.d/next/Library/2024-01-08-23-55-50.gh-issue-76637.U9fXWx.rst
new file mode 100644
index 00000000000000..1e55b96d659e18
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2024-01-08-23-55-50.gh-issue-76637.U9fXWx.rst
@@ -0,0 +1 @@
+Deprecate the ``undefined`` codec. Patch by Victor Stinner.