diff --git a/Lib/test/test_tempfile.py b/Lib/test/test_tempfile.py
index ccf7ea072de276..2632e77fc82dec 100644
--- a/Lib/test/test_tempfile.py
+++ b/Lib/test/test_tempfile.py
@@ -1726,9 +1726,25 @@ def test_modes(self):
                     d.cleanup()
                 self.assertFalse(os.path.exists(d.name))
 
-    @unittest.skipUnless(hasattr(os, 'chflags'), 'requires os.lchflags')
+    @unittest.skipUnless(hasattr(os, 'chflags'), 'requires os.chflags')
     def test_flags(self):
         flags = stat.UF_IMMUTABLE | stat.UF_NOUNLINK
+
+        # skip the test if these flags are not supported (ex: FreeBSD 13)
+        filename = os_helper.TESTFN
+        try:
+            open(filename, "w").close()
+            try:
+                os.chflags(filename, flags)
+            except OSError as exc:
+                # "OSError: [Errno 45] Operation not supported"
+                self.skipTest(f"chflags() doesn't support "
+                              f"UF_IMMUTABLE|UF_NOUNLINK: {exc}")
+            else:
+                os.chflags(filename, 0)
+        finally:
+            os_helper.unlink(filename)
+
         d = self.do_create(recurse=3, dirs=2, files=2)
         with d:
             # Change files and directories flags recursively.
diff --git a/Misc/NEWS.d/next/Tests/2023-09-05-23-00-09.gh-issue-108962.R4NwuU.rst b/Misc/NEWS.d/next/Tests/2023-09-05-23-00-09.gh-issue-108962.R4NwuU.rst
new file mode 100644
index 00000000000000..380fb20b8881b2
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2023-09-05-23-00-09.gh-issue-108962.R4NwuU.rst
@@ -0,0 +1,3 @@
+Skip ``test_tempfile.test_flags()`` if ``chflags()`` fails with "OSError:
+[Errno 45] Operation not supported" (ex: on FreeBSD 13). Patch by Victor
+Stinner.