diff --git a/bump_pydantic/codemods/replace_config.py b/bump_pydantic/codemods/replace_config.py
index 9eef776..9070547 100644
--- a/bump_pydantic/codemods/replace_config.py
+++ b/bump_pydantic/codemods/replace_config.py
@@ -15,7 +15,6 @@
 CHECK_LINK_COMMENT = "# Check https://docs.pydantic.dev/dev-v2/migration/#changes-to-config for more information."
 
 REMOVED_KEYS = [
-    "allow_mutation",
     "error_msg_templates",
     "fields",
     "getter_dict",
@@ -38,6 +37,7 @@
     "orm_mode": "from_attributes",
     "schema_extra": "json_schema_extra",
     "validate_all": "validate_default",
+    "allow_mutation": "frozen",
 }
 
 EXTRA_ATTRIBUTE = m.Attribute(
@@ -164,16 +164,23 @@ def visit_Assign(self, node: cst.Assign) -> None:
         self.assign_value = node.value
 
     def visit_AssignTarget(self, node: cst.AssignTarget) -> None:
-        if self.inside_config_class:
-            keyword = RENAMED_KEYS.get(node.target.value, node.target.value)  # type: ignore[attr-defined]
+        if self.inside_config_class and isinstance(node.target, cst.Name):
+            keyword = RENAMED_KEYS.get(node.target.value, node.target.value)
+            value: cst.BaseExpression
             if m.matches(self.assign_value, EXTRA_ATTRIBUTE):
                 value = cst.SimpleString(value=f'"{self.assign_value.attr.value}"')  # type: ignore[attr-defined]
                 RemoveImportsVisitor.remove_unused_import(self.context, "pydantic", "Extra")
             else:
-                value = self.assign_value  # type: ignore[assignment]
+                value = self.assign_value
+            if node.target.value == "allow_mutation":
+                # The `allow_mutation` keyword is the negative of `frozen`.
+                if m.matches(value, m.Name(value="False")):
+                    value = cst.Name("True")
+                elif m.matches(value, m.Name(value="True")):
+                    value = cst.Name("False")
             self.config_args.append(
                 cst.Arg(
-                    keyword=node.target.with_changes(value=keyword),  # type: ignore[arg-type]
+                    keyword=node.target.with_changes(value=keyword),
                     value=value,
                     equal=cst.AssignEqual(
                         whitespace_before=cst.SimpleWhitespace(""),
diff --git a/tests/unit/test_replace_config.py b/tests/unit/test_replace_config.py
index 8c024a1..e40cb54 100644
--- a/tests/unit/test_replace_config.py
+++ b/tests/unit/test_replace_config.py
@@ -192,21 +192,37 @@ class Potato(BaseModel):
         """
         self.assertCodemod(before, after)
 
+    def test_allow_mutation(self) -> None:
+        before = """
+        from pydantic import BaseModel
+
+        class Potato(BaseModel):
+            class Config:
+                allow_mutation = False
+        """
+        after = """
+        from pydantic import ConfigDict, BaseModel
+
+        class Potato(BaseModel):
+            model_config = ConfigDict(frozen=True)
+        """
+        self.assertCodemod(before, after)
+
     def test_removed_keys(self) -> None:
         before = """
         from pydantic import BaseModel
 
         class Potato(BaseModel):
             class Config:
-                allow_mutation = True
+                underscore_attrs_are_private = True
         """
         after = """
         from pydantic import ConfigDict, BaseModel
 
         class Potato(BaseModel):
-            # TODO[pydantic]: The following keys were removed: `allow_mutation`.
+            # TODO[pydantic]: The following keys were removed: `underscore_attrs_are_private`.
             # Check https://docs.pydantic.dev/dev-v2/migration/#changes-to-config for more information.
-            model_config = ConfigDict(allow_mutation=True)
+            model_config = ConfigDict(underscore_attrs_are_private=True)
         """
         self.assertCodemod(before, after)
 
@@ -216,16 +232,16 @@ def test_multiple_removed_keys(self) -> None:
 
         class Potato(BaseModel):
             class Config:
-                allow_mutation = True
+                underscore_attrs_are_private = True
                 smart_union = True
         """
         after = """
         from pydantic import ConfigDict, BaseModel
 
         class Potato(BaseModel):
-            # TODO[pydantic]: The following keys were removed: `allow_mutation`, `smart_union`.
+            # TODO[pydantic]: The following keys were removed: `underscore_attrs_are_private`, `smart_union`.
             # Check https://docs.pydantic.dev/dev-v2/migration/#changes-to-config for more information.
-            model_config = ConfigDict(allow_mutation=True, smart_union=True)
+            model_config = ConfigDict(underscore_attrs_are_private=True, smart_union=True)
         """
         self.assertCodemod(before, after)