diff --git a/flax/linen/module.py b/flax/linen/module.py
index 1b913d51a..f106e14b9 100644
--- a/flax/linen/module.py
+++ b/flax/linen/module.py
@@ -862,6 +862,8 @@ def __set_name__(self, *args, **kwargs):
         self.wrapped.__set_name__(*args, **kwargs)
 
     def __getattr__(self, name):
+      if 'wrapped' not in vars(self):
+        raise AttributeError()
       return getattr(self.wrapped, name)
 
   return _DescriptorWrapper(descriptor)
diff --git a/tests/linen/linen_module_test.py b/tests/linen/linen_module_test.py
index c0f1b211f..da49524e2 100644
--- a/tests/linen/linen_module_test.py
+++ b/tests/linen/linen_module_test.py
@@ -22,6 +22,7 @@
 import inspect
 import operator
 import sys
+from tempfile import TemporaryDirectory
 from typing import (
     Any,
     Callable,
@@ -2399,6 +2400,31 @@ def record_interceptor(f, args, kwargs, context):
     self.assertIs(called[0], bar)
     self.assertIs(called[1], foo)
 
+  def test_cloudpickle_module(self):
+    from cloudpickle import cloudpickle_fast
+
+    class NNModuleWithProperty(nn.Module):
+      a: int
+      b: str
+
+      @property
+      def my_property(self):
+        return self.b * self.a
+
+    m = NNModuleWithProperty(a=2, b='ok')
+
+    with TemporaryDirectory() as tmpdir:
+      filename = f'{tmpdir}/module.pkl'
+      with open(filename, 'wb') as f:
+        cloudpickle_fast.dump(m, f)
+
+      with open(filename, 'rb') as f:
+        obj_loaded = cloudpickle_fast.load(f)
+
+    self.assertEqual(obj_loaded.a, 2)
+    self.assertEqual(obj_loaded.b, 'ok')
+    self.assertEqual(obj_loaded.my_property, 'okok')
+
 
 class LeakTests(absltest.TestCase):