diff --git a/Lib/test/test_typing.py b/Lib/test/test_typing.py
index 0910fd4022e..d203ce3d598 100644
--- a/Lib/test/test_typing.py
+++ b/Lib/test/test_typing.py
@@ -896,6 +896,44 @@ class GenericTests(BaseTestCase):
             self.assertEqual(t, copy(t))
             self.assertEqual(t, deepcopy(t))
 
+    def test_parameterized_slots(self):
+        T = TypeVar('T')
+        class C(Generic[T]):
+            __slots__ = ('potato',)
+
+        c = C()
+        c_int = C[int]()
+        self.assertEqual(C.__slots__, C[str].__slots__)
+
+        c.potato = 0
+        c_int.potato = 0
+        with self.assertRaises(AttributeError):
+            c.tomato = 0
+        with self.assertRaises(AttributeError):
+            c_int.tomato = 0
+
+        def foo(x: C['C']): ...
+        self.assertEqual(get_type_hints(foo, globals(), locals())['x'], C[C])
+        self.assertEqual(get_type_hints(foo, globals(), locals())['x'].__slots__,
+                         C.__slots__)
+        self.assertEqual(copy(C[int]), deepcopy(C[int]))
+
+    def test_parameterized_slots_dict(self):
+        T = TypeVar('T')
+        class D(Generic[T]):
+            __slots__ = {'banana': 42}
+
+        d = D()
+        d_int = D[int]()
+        self.assertEqual(D.__slots__, D[str].__slots__)
+
+        d.banana = 'yes'
+        d_int.banana = 'yes'
+        with self.assertRaises(AttributeError):
+            d.foobar = 'no'
+        with self.assertRaises(AttributeError):
+            d_int.foobar = 'no'
+
     def test_errors(self):
         with self.assertRaises(TypeError):
             B = SimpleMapping[XK, Any]
diff --git a/Lib/typing.py b/Lib/typing.py
index 1a943aca20a..34845b747a2 100644
--- a/Lib/typing.py
+++ b/Lib/typing.py
@@ -870,6 +870,17 @@ def _make_subclasshook(cls):
     return __extrahook__
 
 
+def _no_slots_copy(dct):
+    """Internal helper: copy class __dict__ and clean slots class variables.
+    (They will be re-created if necessary by normal class machinery.)
+    """
+    dict_copy = dict(dct)
+    if '__slots__' in dict_copy:
+        for slot in dict_copy['__slots__']:
+            dict_copy.pop(slot, None)
+    return dict_copy
+
+
 class GenericMeta(TypingMeta, abc.ABCMeta):
     """Metaclass for generic types."""
 
@@ -967,7 +978,7 @@ class GenericMeta(TypingMeta, abc.ABCMeta):
             return self
         return self.__class__(self.__name__,
                               self.__bases__,
-                              dict(self.__dict__),
+                              _no_slots_copy(self.__dict__),
                               tvars=_type_vars(ev_args) if ev_args else None,
                               args=ev_args,
                               origin=ev_origin,
@@ -1043,7 +1054,7 @@ class GenericMeta(TypingMeta, abc.ABCMeta):
             args = params
         return self.__class__(self.__name__,
                               self.__bases__,
-                              dict(self.__dict__),
+                              _no_slots_copy(self.__dict__),
                               tvars=tvars,
                               args=args,
                               origin=self,
@@ -1059,7 +1070,8 @@ class GenericMeta(TypingMeta, abc.ABCMeta):
         return issubclass(instance.__class__, self)
 
     def __copy__(self):
-        return self.__class__(self.__name__, self.__bases__, dict(self.__dict__),
+        return self.__class__(self.__name__, self.__bases__,
+                              _no_slots_copy(self.__dict__),
                               self.__parameters__, self.__args__, self.__origin__,
                               self.__extra__, self.__orig_bases__)