diff --git a/src/mcp/server/auth/middleware/bearer_auth.py b/src/mcp/server/auth/middleware/bearer_auth.py
index 300b29892..26ac21192 100644
--- a/src/mcp/server/auth/middleware/bearer_auth.py
+++ b/src/mcp/server/auth/middleware/bearer_auth.py
@@ -113,16 +113,26 @@ async def __call__(self, scope: Scope, receive: Receive, send: Send) -> None:
             # auth_credentials should always be provided; this is just paranoia
             if auth_credentials is None or required_scope not in auth_credentials.scopes:
                 await self._send_auth_error(
-                    send, status_code=403, error="insufficient_scope", description=f"Required scope: {required_scope}"
+                    send,
+                    status_code=403,
+                    error="insufficient_scope",
+                    description=f"Required scope: {required_scope}",
+                    # RFC 6750 3.1: on insufficient_scope, the challenge MAY carry the
+                    # scope necessary to access the resource.
+                    scope=" ".join(self.required_scopes),
                 )
                 return
 
         await self.app(scope, receive, send)
 
-    async def _send_auth_error(self, send: Send, status_code: int, error: str, description: str) -> None:
+    async def _send_auth_error(
+        self, send: Send, status_code: int, error: str, description: str, scope: str | None = None
+    ) -> None:
         """Send an authentication error response with WWW-Authenticate header."""
         # Build WWW-Authenticate header value
         www_auth_parts = [f'error="{error}"', f'error_description="{description}"']
+        if scope:
+            www_auth_parts.append(f'scope="{scope}"')
         if self.resource_metadata_url:  # pragma: no cover
             www_auth_parts.append(f'resource_metadata="{self.resource_metadata_url}"')
 
diff --git a/tests/server/auth/middleware/test_bearer_auth.py b/tests/server/auth/middleware/test_bearer_auth.py
index e13ab9639..83c2a5b0b 100644
--- a/tests/server/auth/middleware/test_bearer_auth.py
+++ b/tests/server/auth/middleware/test_bearer_auth.py
@@ -346,6 +346,54 @@ async def send(message: Message) -> None:
         assert any(h[0] == b"www-authenticate" for h in sent_messages[0]["headers"])
         assert not app.called
 
+    async def test_missing_required_scope_includes_scope_in_challenge(self, valid_access_token: AccessToken):
+        """RFC 6750 3.1: an insufficient_scope challenge MAY include the required scope."""
+        app = MockApp()
+        middleware = RequireAuthMiddleware(app, required_scopes=["admin", "superuser"])
+
+        # Create a user with read/write scopes but neither required scope
+        user = AuthenticatedUser(valid_access_token)
+        auth = AuthCredentials(["read", "write"])
+
+        scope: Scope = {"type": "http", "user": user, "auth": auth}
+
+        async def receive() -> Message:  # pragma: no cover
+            return {"type": "http.request"}
+
+        sent_messages: list[Message] = []
+
+        async def send(message: Message) -> None:
+            sent_messages.append(message)
+
+        await middleware(scope, receive, send)
+
+        assert sent_messages[0]["status"] == 403
+        www_authenticate = next(h[1] for h in sent_messages[0]["headers"] if h[0] == b"www-authenticate")
+        assert www_authenticate == (
+            b'Bearer error="insufficient_scope", error_description="Required scope: admin", scope="admin superuser"'
+        )
+        assert not app.called
+
+    async def test_no_user_challenge_omits_scope(self):
+        """RFC 6750 3.1: scope is specific to insufficient_scope; a bare 401 challenge should not carry it."""
+        app = MockApp()
+        middleware = RequireAuthMiddleware(app, required_scopes=["read"])
+        scope: Scope = {"type": "http"}
+
+        async def receive() -> Message:  # pragma: no cover
+            return {"type": "http.request"}
+
+        sent_messages: list[Message] = []
+
+        async def send(message: Message) -> None:
+            sent_messages.append(message)
+
+        await middleware(scope, receive, send)
+
+        assert sent_messages[0]["status"] == 401
+        www_authenticate = next(h[1] for h in sent_messages[0]["headers"] if h[0] == b"www-authenticate")
+        assert b"scope=" not in www_authenticate
+
     async def test_no_auth_credentials(self, valid_access_token: AccessToken):
         """Test middleware with no auth credentials in scope."""
         app = MockApp()