diff --git a/sklearn/utils/estimator_checks.py b/sklearn/utils/estimator_checks.py
index 3c9f6371e0a1e..bbfd12ad39b9c 100644
--- a/sklearn/utils/estimator_checks.py
+++ b/sklearn/utils/estimator_checks.py
@@ -1,4 +1,3 @@
-import types
 import warnings
 import pickle
 import re
@@ -3297,18 +3296,25 @@ def param_filter(p):
                 tuple,
                 type(None),
                 type,
-                types.FunctionType,
-                joblib.Memory,
             }
             # Any numpy numeric such as np.int32.
             allowed_types.update(np.core.numerictypes.allTypes.values())
-            assert type(init_param.default) in allowed_types, (
+
+            allowed_value = (
+                type(init_param.default) in allowed_types
+                or
+                # Although callables are mutable, we accept them as argument
+                # default value and trust that neither the implementation of
+                # the callable nor of the estimator changes the state of the
+                # callable.
+                callable(init_param.default)
+            )
+
+            assert allowed_value, (
                 f"Parameter '{init_param.name}' of estimator "
                 f"'{Estimator.__name__}' is of type "
-                f"{type(init_param.default).__name__} which is not "
-                "allowed. All init parameters have to be immutable to "
-                "make cloning possible. Therefore we restrict the set of "
-                "legal types to "
+                f"{type(init_param.default).__name__} which is not allowed. "
+                f"'{init_param.name}' must be a callable or must be of type "
                 f"{set(type.__name__ for type in allowed_types)}."
             )
             if init_param.name not in params.keys():