diff --git a/samtranslator/model/api/websocket_api_generator.py b/samtranslator/model/api/websocket_api_generator.py
index ff3d249c2..9fe71e0fd 100644
--- a/samtranslator/model/api/websocket_api_generator.py
+++ b/samtranslator/model/api/websocket_api_generator.py
@@ -32,7 +32,7 @@ class WebSocketApiGenerator(ApiV2Generator):
     def __init__(  # noqa: PLR0913
         self,
         logical_id: str,
-        stage_name: str | None,
+        stage_name: Intrinsicable[str] | None,
         stage_variables: (
             dict[str, Intrinsicable[str]] | None
         ),  # I tried to keep presence of = None consistent with http
@@ -295,14 +295,23 @@ def _construct_permission(self, route_key: str, perms_id: str, route_spec: dict[
         perms.Action = "lambda:InvokeFunction"
         perms.FunctionName = route_spec["FunctionArn"]
         perms.Principal = "apigateway.amazonaws.com"
-        perms.SourceArn = fnSub(
-            "arn:${AWS::Partition}:execute-api:${AWS::Region}:${AWS::AccountId}:${"
-            + self.logical_id
-            + ".ApiId}/"
-            + self.stage_name
-            + "/"
-            + route_key
-        )
+        if isinstance(self.stage_name, str):
+            perms.SourceArn = fnSub(
+                "arn:${AWS::Partition}:execute-api:${AWS::Region}:${AWS::AccountId}:${"
+                + self.logical_id
+                + ".ApiId}/"
+                + self.stage_name
+                + "/"
+                + route_key
+            )
+        else:
+            perms.SourceArn = fnSub(
+                "arn:${AWS::Partition}:execute-api:${AWS::Region}:${AWS::AccountId}:${"
+                + self.logical_id
+                + ".ApiId}/${__StageName__}/"
+                + route_key,
+                {"__StageName__": self.stage_name},
+            )
         return perms
 
     def _construct_route_infr(self, route_key: str, route_spec: dict[str, Any]) -> tuple[
diff --git a/samtranslator/model/sam_resources.py b/samtranslator/model/sam_resources.py
index 7fccf78b5..0a3a9ba29 100644
--- a/samtranslator/model/sam_resources.py
+++ b/samtranslator/model/sam_resources.py
@@ -1910,7 +1910,7 @@ class SamWebSocketApi(SamResourceMacro):
         "Routes": PropertyType(True, IS_DICT),
         "RouteSettings": PropertyType(False, IS_DICT),
         "RouteSelectionExpression": PropertyType(True, IS_STR),
-        "StageName": PropertyType(False, IS_STR),
+        "StageName": PropertyType(False, one_of(IS_STR, IS_DICT)),
         "StageVariables": PropertyType(False, IS_DICT),
         "Tags": PropertyType(False, IS_DICT),
     }
@@ -1930,7 +1930,7 @@ class SamWebSocketApi(SamResourceMacro):
     Routes: dict[str, dict[str, Any]]
     RouteSettings: dict[str, Any] | None
     RouteSelectionExpression: str
-    StageName: str | None
+    StageName: Intrinsicable[str] | None
     StageVariables: dict[str, Intrinsicable[str]] | None
     Tags: dict[str, Any] | None
 
diff --git a/tests/model/api/test_websocket_api_generator.py b/tests/model/api/test_websocket_api_generator.py
index ec2a5434c..7a37a4786 100644
--- a/tests/model/api/test_websocket_api_generator.py
+++ b/tests/model/api/test_websocket_api_generator.py
@@ -47,6 +47,16 @@ def test_perms(self):
             "arn:${AWS::Partition}:execute-api:${AWS::Region}:${AWS::AccountId}:${WebSocketApiId.ApiId}/default/$connect",
         )
 
+    def test_perms_with_intrinsic_stage_name(self):
+        """Test that _construct_permission handles intrinsic StageName without TypeError."""
+        kwargs = self.kwargs.copy()
+        kwargs["stage_name"] = {"Ref": "StageName"}
+        _, _, perm, _ = WebSocketApiGenerator(**kwargs)._construct_route_infr("$connect", kwargs["routes"]["$connect"])
+        fn_sub = perm.SourceArn["Fn::Sub"]
+        self.assertIsInstance(fn_sub, list)
+        self.assertIn("${__StageName__}", fn_sub[0])
+        self.assertEqual(fn_sub[1]["__StageName__"], {"Ref": "StageName"})
+
     def test_none_auth_no_id(self):
         kwargs = self.kwargs.copy()
         kwargs["auth_config"] = {"AuthType": "NONE"}