diff --git a/mypy/checkmember.py b/mypy/checkmember.py
@@ -716,7 +716,11 @@ def analyze_class_attribute_access(itype: Instance,
             if isinstance(t, TypeVarType) or get_type_vars(t):
                 # Exception: access on Type[...], including first argument of class methods is OK.
                 if not isinstance(get_proper_type(mx.original_type), TypeType):
-                    mx.msg.fail(message_registry.GENERIC_INSTANCE_VAR_CLASS_ACCESS, mx.context)
+                    if node.node.is_classvar:
+                        message = message_registry.GENERIC_CLASS_VAR_ACCESS
+                    else:
+                        message = message_registry.GENERIC_INSTANCE_VAR_CLASS_ACCESS
+                    mx.msg.fail(message, mx.context)
 
             # Erase non-mapped variables, but keep mapped ones, even if there is an error.
             # In the above example this means that we infer following types:

diff --git a/mypy/message_registry.py b/mypy/message_registry.py
@@ -88,6 +88,8 @@
 # Generic
 GENERIC_INSTANCE_VAR_CLASS_ACCESS = \
     'Access to generic instance variables via class is ambiguous'  # type: Final
+GENERIC_CLASS_VAR_ACCESS = \
+    'Access to generic class variables is ambiguous'  # type: Final
 BARE_GENERIC = 'Missing type parameters for generic type {}'  # type: Final
 IMPLICIT_GENERIC_ANY_BUILTIN = \
     'Implicit generic "Any". Use "{}" and specify generic parameters'  # type: Final

diff --git a/mypy/typeanal.py b/mypy/typeanal.py
@@ -15,8 +15,8 @@
     Type, UnboundType, TypeVarType, TupleType, TypedDictType, UnionType, Instance, AnyType,
     CallableType, NoneType, ErasedType, DeletedType, TypeList, TypeVarDef, SyntheticTypeVisitor,
     StarType, PartialType, EllipsisType, UninhabitedType, TypeType, replace_alias_tvars,
-    CallableArgument, get_type_vars, TypeQuery, union_items, TypeOfAny,
-    LiteralType, RawExpressionType, PlaceholderType, Overloaded, get_proper_type, ProperType
+    CallableArgument, TypeQuery, union_items, TypeOfAny, LiteralType, RawExpressionType,
+    PlaceholderType, Overloaded, get_proper_type, ProperType
 )
 
 from mypy.nodes import (
@@ -311,9 +311,6 @@ def try_analyze_special_unbound_type(self, t: UnboundType, fullname: str) -> Opt
                 self.fail('ClassVar[...] must have at most one type argument', t)
                 return AnyType(TypeOfAny.from_error)
             item = self.anal_type(t.args[0])
-            if isinstance(item, TypeVarType) or get_type_vars(item):
-                self.fail('Invalid type: ClassVar cannot be generic', t)
-                return AnyType(TypeOfAny.from_error)
             return item
         elif fullname in ('mypy_extensions.NoReturn', 'typing.NoReturn'):
             return UninhabitedType(is_noreturn=True)

diff --git a/test-data/unit/check-classvar.test b/test-data/unit/check-classvar.test
@@ -280,3 +280,48 @@ class A:
 [out]
 main:2: note: Revealed type is 'builtins.int'
 main:3: error: Cannot assign to class variable "x" via instance
+
+[case testClassVarWithGeneric]
+from typing import ClassVar, Generic, TypeVar
+T = TypeVar('T')
+class A(Generic[T]):
+    x: ClassVar[T]
+    @classmethod
+    def foo(cls) -> T:
+        return cls.x  # OK
+
+A.x  # E: Access to generic class variables is ambiguous
+A.x = 1  # E: Access to generic class variables is ambiguous
+A[int].x  # E: Access to generic class variables is ambiguous
+
+class Bad(A[int]):
+    pass
+Bad.x  # E: Access to generic class variables is ambiguous
+
+class Good(A[int]):
+    x = 42
+reveal_type(Good.x)  # N: Revealed type is 'builtins.int'
+[builtins fixtures/classmethod.pyi]
+
+[case testClassVarWithNestedGeneric]
+from typing import ClassVar, Generic, Tuple, TypeVar, Union, Type
+T = TypeVar('T')
+U = TypeVar('U')
+class A(Generic[T, U]):
+    x: ClassVar[Union[T, Tuple[U, Type[U]]]]
+    @classmethod
+    def foo(cls) -> Union[T, Tuple[U, Type[U]]]:
+        return cls.x  # OK
+
+A.x  # E: Access to generic class variables is ambiguous
+A.x = 1  # E: Access to generic class variables is ambiguous
+A[int, str].x  # E: Access to generic class variables is ambiguous
+
+class Bad(A[int, str]):
+    pass
+Bad.x  # E: Access to generic class variables is ambiguous
+
+class Good(A[int, str]):
+    x = 42
+reveal_type(Good.x)  # N: Revealed type is 'builtins.int'
+[builtins fixtures/classmethod.pyi]
diff --git a/test-data/unit/semanal-classvar.test b/test-data/unit/semanal-classvar.test
@@ -206,21 +206,3 @@ class B:
         pass
 [out]
 main:4: error: ClassVar can only be used for assignments in class body
-
-[case testClassVarWithGeneric]
-from typing import ClassVar, Generic, TypeVar
-T = TypeVar('T')
-class A(Generic[T]):
-    x = None  # type: ClassVar[T]
-[out]
-main:4: error: Invalid type: ClassVar cannot be generic
-
-[case testClassVarWithNestedGeneric]
-from typing import ClassVar, Generic, List, TypeVar, Union
-T = TypeVar('T')
-U = TypeVar('U')
-class A(Generic[T, U]):
-    x = None  # type: ClassVar[Union[T, List[U]]]
-[builtins fixtures/list.pyi]
-[out]
-main:5: error: Invalid type: ClassVar cannot be generic