diff --git a/cloudpickle/cloudpickle.py b/cloudpickle/cloudpickle.py
index 4f4d857a..5a74cce5 100644
--- a/cloudpickle/cloudpickle.py
+++ b/cloudpickle/cloudpickle.py
@@ -751,6 +751,14 @@ def _class_getstate(obj):
     clsdict = _extract_class_dict(obj)
     clsdict.pop("__weakref__", None)
 
+    # In Python 3.13+, classes with annotations have an __annotate__ function
+    # that may have closures referencing unpicklable objects in the class
+    # namespace. We don't need to pickle it as Python will regenerate it from
+    # __annotations__ when the class is reconstructed.
+    clsdict.pop("__annotate__", None)
+    # Also handle __annotate_func__ which may appear in some Python 3.14 builds
+    clsdict.pop("__annotate_func__", None)
+
     if issubclass(type(obj), abc.ABCMeta):
         # If obj is an instance of an ABCMeta subclass, don't pickle the
         # cache/negative caches populated during isinstance/issubclass
diff --git a/tests/cloudpickle_test.py b/tests/cloudpickle_test.py
index 45e8c592..7640cf4e 100644
--- a/tests/cloudpickle_test.py
+++ b/tests/cloudpickle_test.py
@@ -1429,6 +1429,33 @@ def some_method(self):
 
         self.assertRaises(TypeError, IncompleteBaseSubclass)
 
+    def test_abc_with_annotations(self):
+        # Test pickling abstract classes with type annotations.
+        # This is a regression test for Python 3.13+ (PEP 649) where __annotate__
+        # functions can have closures that reference _abc_impl.
+
+        def class_factory():
+            class Model(abc.ABC):
+                field1: int
+                field2: str
+                field3: float
+
+            return Model
+
+        Model = class_factory()
+
+        # This should not raise TypeError about unpicklable _abc._abc_data
+        depickled = pickle_depickle(Model, protocol=self.protocol)
+
+        # Verify the annotations are preserved
+        self.assertEqual(
+            depickled.__annotations__,
+            {"field1": int, "field2": str, "field3": float},
+        )
+
+        # Verify it's still an ABC
+        self.assertTrue(issubclass(depickled, abc.ABC))
+
     def test_weakset_identity_preservation(self):
         # Test that weaksets don't lose all their inhabitants if they're
         # pickled in a larger data structure that includes other references to