diff --git a/mypy/messages.py b/mypy/messages.py
index e11ee9d0f7f29..ebe76509c1b65 100644
--- a/mypy/messages.py
+++ b/mypy/messages.py
@@ -2658,6 +2658,7 @@ def get_bad_protocol_flags(
         if (
             IS_CLASSVAR in subflags
             and IS_CLASSVAR not in superflags
+            and IS_SETTABLE in superflags
             or IS_CLASSVAR in superflags
             and IS_CLASSVAR not in subflags
             or IS_SETTABLE in superflags
diff --git a/mypy/subtypes.py b/mypy/subtypes.py
index 9a4982f5b8ecb..b4f948c6a9c1e 100644
--- a/mypy/subtypes.py
+++ b/mypy/subtypes.py
@@ -1027,7 +1027,10 @@ def named_type(fullname: str) -> Instance:
                 if not is_subtype(supertype, subtype):
                     return False
             if not class_obj:
-                if (IS_CLASSVAR in subflags) != (IS_CLASSVAR in superflags):
+                if IS_SETTABLE not in superflags:
+                    if IS_CLASSVAR in superflags and IS_CLASSVAR not in subflags:
+                        return False
+                elif (IS_CLASSVAR in subflags) != (IS_CLASSVAR in superflags):
                     return False
             else:
                 if IS_VAR in superflags and IS_CLASSVAR not in subflags:
diff --git a/test-data/unit/check-protocols.test b/test-data/unit/check-protocols.test
index 113b2000fc227..ec7bf8816f341 100644
--- a/test-data/unit/check-protocols.test
+++ b/test-data/unit/check-protocols.test
@@ -1153,6 +1153,25 @@ x2 = y2 # E: Incompatible types in assignment (expression has type "PP", variabl
         # N: Protocol member P.attr expected settable variable, got read-only attribute
 [builtins fixtures/property.pyi]
 
+[case testClassVarProtocolImmutable]
+from typing import Protocol, ClassVar
+
+class P(Protocol):
+    @property
+    def x(self) -> int: ...
+
+class C:
+    x: ClassVar[int]
+
+class Bad:
+    x: ClassVar[str]
+
+x: P = C()
+y: P = Bad()  # E: Incompatible types in assignment (expression has type "Bad", variable has type "P") \
+              # N: Following member(s) of "Bad" have conflicts: \
+              # N:     x: expected "int", got "str"
+[builtins fixtures/property.pyi]
+
 [case testSettablePropertyInProtocols]
 from typing import Protocol