diff --git a/Lib/test/test_socket.py b/Lib/test/test_socket.py
index b36cb5beaec859..1957149cac97f6 100755
--- a/Lib/test/test_socket.py
+++ b/Lib/test/test_socket.py
@@ -6390,12 +6390,16 @@ def test_sha256(self):
                 self.assertEqual(op.recv(512), expected)
 
     def test_hmac_sha1(self):
-        expected = bytes.fromhex("effcdf6ae5eb2fa2d27416d5f184df9c259a7c79")
+        # gh-109396: In FIPS mode, Linux 6.5 requires a key
+        # of at least 112 bits. Use a key of 152 bits.
+        key = b"Python loves AF_ALG"
+        data = b"what do ya want for nothing?"
+        expected = bytes.fromhex("193dbb43c6297b47ea6277ec0ce67119a3f3aa66")
         with self.create_alg('hash', 'hmac(sha1)') as algo:
-            algo.setsockopt(socket.SOL_ALG, socket.ALG_SET_KEY, b"Jefe")
+            algo.setsockopt(socket.SOL_ALG, socket.ALG_SET_KEY, key)
             op, _ = algo.accept()
             with op:
-                op.sendall(b"what do ya want for nothing?")
+                op.sendall(data)
                 self.assertEqual(op.recv(512), expected)
 
     # Although it should work with 3.19 and newer the test blocks on
diff --git a/Misc/NEWS.d/next/Tests/2023-09-14-22-58-47.gh-issue-109396.J1a4jR.rst b/Misc/NEWS.d/next/Tests/2023-09-14-22-58-47.gh-issue-109396.J1a4jR.rst
new file mode 100644
index 00000000000000..71150ecae76434
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2023-09-14-22-58-47.gh-issue-109396.J1a4jR.rst
@@ -0,0 +1,3 @@
+Fix ``test_socket.test_hmac_sha1()`` in FIPS mode. Use a longer key: FIPS
+mode requires at least of at least 112 bits. The previous key was only 32
+bits. Patch by Victor Stinner.