Index: src/wp-includes/class-wp-customize-nav-menus.php
===================================================================
--- src/wp-includes/class-wp-customize-nav-menus.php	(revision 38677)
+++ src/wp-includes/class-wp-customize-nav-menus.php	(working copy)
@@ -764,6 +764,10 @@
 			wp_send_json_error( 'missing_params', 400 );
 		}
 
+		if ( ! apply_filters( 'customize_create_nav_menu_content', true ) ) {
+			wp_send_json_error( 'nav_menu_creation_disabled', 400 );
+		}
+
 		$params = wp_array_slice_assoc(
 			array_merge(
 				array(
@@ -941,7 +945,7 @@
 					<div class="accordion-section-content">
 						<?php if ( 'post_type' === $available_item_type['type'] ) : ?>
 							<?php $post_type_obj = get_post_type_object( $available_item_type['object'] ); ?>
-							<?php if ( current_user_can( $post_type_obj->cap->create_posts ) && current_user_can( $post_type_obj->cap->publish_posts ) ) : ?>
+							<?php if ( current_user_can( $post_type_obj->cap->create_posts ) && current_user_can( $post_type_obj->cap->publish_posts ) && apply_filters( 'customize_create_nav_menu_content', true ) ) : ?>
 								<div class="new-content-item">
 									<input type="text" class="create-item-input" placeholder="<?php echo esc_attr( $post_type_obj->labels->add_new_item ); ?>">
 									<button type="button" class="button add-content"><?php _e( 'Add' ); ?></button>