diff --git a/mypy/plugins/dataclasses.py b/mypy/plugins/dataclasses.py
index 211f0a8dda83..18caed8bbb8e 100644
--- a/mypy/plugins/dataclasses.py
+++ b/mypy/plugins/dataclasses.py
@@ -210,6 +210,7 @@ def transform(self) -> None:
                 )
 
         if decorator_arguments['frozen']:
+            self._propertize_callables(attributes, settable=False)
             self._freeze(attributes)
         else:
             self._propertize_callables(attributes)
@@ -466,7 +467,9 @@ def _freeze(self, attributes: List[DataclassAttribute]) -> None:
                 var._fullname = info.fullname + '.' + var.name
                 info.names[var.name] = SymbolTableNode(MDEF, var)
 
-    def _propertize_callables(self, attributes: List[DataclassAttribute]) -> None:
+    def _propertize_callables(self,
+                              attributes: List[DataclassAttribute],
+                              settable: bool = True) -> None:
         """Converts all attributes with callable types to @property methods.
 
         This avoids the typechecker getting confused and thinking that
@@ -480,7 +483,7 @@ def _propertize_callables(self, attributes: List[DataclassAttribute]) -> None:
                 var = attr.to_var()
                 var.info = info
                 var.is_property = True
-                var.is_settable_property = True
+                var.is_settable_property = settable
                 var._fullname = info.fullname + '.' + var.name
                 info.names[var.name] = SymbolTableNode(MDEF, var)
 
diff --git a/test-data/unit/check-dataclasses.test b/test-data/unit/check-dataclasses.test
index 1773ac0eac8d..1ccf2c4d444e 100644
--- a/test-data/unit/check-dataclasses.test
+++ b/test-data/unit/check-dataclasses.test
@@ -1537,6 +1537,22 @@ A(1)
 A(a="foo")  # E: Argument "a" to "A" has incompatible type "str"; expected "int"
 [builtins fixtures/dataclasses.pyi]
 
+[case testDataclassesCallableFrozen]
+# flags: --python-version 3.7
+from dataclasses import dataclass
+from typing import Any, Callable
+@dataclass(frozen=True)
+class A:
+    a: Callable[..., None]
+
+def func() -> None:
+    pass
+
+reveal_type(A.a)  # N: Revealed type is "def (*Any, **Any)"
+A(a=func).a()
+A(a=func).a = func  # E: Property "a" defined in "A" is read-only
+[builtins fixtures/dataclasses.pyi]
+
 [case testDataclassesMultipleInheritanceWithNonDataclass]
 # flags: --python-version 3.10
 from dataclasses import dataclass