diff --git a/packages/edit-site/src/components/sidebar-navigation-screen-navigation-menus/leaf-more-menu.js b/packages/edit-site/src/components/sidebar-navigation-screen-navigation-menus/leaf-more-menu.js
index 14d78405b3abe5..6b093ad27e25b9 100644
--- a/packages/edit-site/src/components/sidebar-navigation-screen-navigation-menus/leaf-more-menu.js
+++ b/packages/edit-site/src/components/sidebar-navigation-screen-navigation-menus/leaf-more-menu.js
@@ -126,16 +126,17 @@ export default function LeafMoreMenu( props ) {
>
{ __( 'Move down' ) }
- { block.attributes?.id && (
-
- ) }
+ { block.attributes?.type === 'page' &&
+ block.attributes?.id && (
+
+ ) }