diff --git a/Lib/inspect.py b/Lib/inspect.py
index 655b04b0eed4d5..8c5f921936aa38 100644
--- a/Lib/inspect.py
+++ b/Lib/inspect.py
@@ -748,18 +748,14 @@ def unwrap(func, *, stop=None):
    :exc:`ValueError` is raised if a cycle is encountered.
 
     """
-    if stop is None:
-        def _is_wrapper(f):
-            return hasattr(f, '__wrapped__')
-    else:
-        def _is_wrapper(f):
-            return hasattr(f, '__wrapped__') and not stop(f)
     f = func  # remember the original func for error reporting
     # Memoise by id to tolerate non-hashable objects, but store objects to
     # ensure they aren't destroyed, which would allow their IDs to be reused.
     memo = {id(f): f}
     recursion_limit = sys.getrecursionlimit()
-    while _is_wrapper(func):
+    while not isinstance(func, type) and hasattr(func, '__wrapped__'):
+        if stop is not None and stop(func):
+            break
         func = func.__wrapped__
         id_func = id(func)
         if (id_func in memo) or (len(memo) >= recursion_limit):
diff --git a/Lib/test/test_inspect/test_inspect.py b/Lib/test/test_inspect/test_inspect.py
index 84cdd25cb7879b..914bb7d43a59b4 100644
--- a/Lib/test/test_inspect/test_inspect.py
+++ b/Lib/test/test_inspect/test_inspect.py
@@ -3273,16 +3273,20 @@ class Bar(Spam, Foo):
                          ((('a', ..., ..., "positional_or_keyword"),),
                           ...))
 
-        class Wrapped:
-            pass
-        Wrapped.__wrapped__ = lambda a: None
-        self.assertEqual(self.signature(Wrapped),
+    def test_signature_on_wrapper(self):
+        class Wrapper:
+            def __call__(self, b):
+                pass
+        wrapper = Wrapper()
+        wrapper.__wrapped__ = lambda a: None
+        self.assertEqual(self.signature(wrapper),
                          ((('a', ..., ..., "positional_or_keyword"),),
                           ...))
         # wrapper loop:
-        Wrapped.__wrapped__ = Wrapped
+        wrapper = Wrapper()
+        wrapper.__wrapped__ = wrapper
         with self.assertRaisesRegex(ValueError, 'wrapper loop'):
-            self.signature(Wrapped)
+            self.signature(wrapper)
 
     def test_signature_on_lambdas(self):
         self.assertEqual(self.signature((lambda a=10: a)),
@@ -4433,6 +4437,14 @@ def test_recursion_limit(self):
         with self.assertRaisesRegex(ValueError, 'wrapper loop'):
             inspect.unwrap(obj)
 
+    def test_wrapped_descriptor(self):
+        self.assertIs(inspect.unwrap(NTimesUnwrappable), NTimesUnwrappable)
+        self.assertIs(inspect.unwrap(staticmethod), staticmethod)
+        self.assertIs(inspect.unwrap(classmethod), classmethod)
+        self.assertIs(inspect.unwrap(staticmethod(classmethod)), classmethod)
+        self.assertIs(inspect.unwrap(classmethod(staticmethod)), staticmethod)
+
+
 class TestMain(unittest.TestCase):
     def test_only_source(self):
         module = importlib.import_module('unittest')
diff --git a/Misc/NEWS.d/next/Library/2024-02-15-23-42-54.gh-issue-112006.4wxcK-.rst b/Misc/NEWS.d/next/Library/2024-02-15-23-42-54.gh-issue-112006.4wxcK-.rst
new file mode 100644
index 00000000000000..7e9fe97a72b5eb
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2024-02-15-23-42-54.gh-issue-112006.4wxcK-.rst
@@ -0,0 +1,2 @@
+Fix :func:`inspect.unwrap` for types with the ``__wrapper__`` data
+descriptor.