Index: src/wp-admin/css/customize-nav-menus.css
===================================================================
--- src/wp-admin/css/customize-nav-menus.css	(revision 39476)
+++ src/wp-admin/css/customize-nav-menus.css	(working copy)
@@ -719,6 +719,10 @@
 	opacity: 0.4;
 }
 
+body.adding-menu-items #customize-preview iframe {
+	pointer-events: none;
+}
+
 .menu-item-handle .spinner {
 	display: none;
 	float: left;
Index: src/wp-admin/js/customize-nav-menus.js
===================================================================
--- src/wp-admin/js/customize-nav-menus.js	(revision 39476)
+++ src/wp-admin/js/customize-nav-menus.js	(working copy)
@@ -666,6 +666,8 @@
 
 		// Opens the panel.
 		open: function( menuControl ) {
+			var self = this;
+
 			this.currentMenuControl = menuControl;
 
 			this.itemSectionHeight();
@@ -672,6 +674,11 @@
 
 			$( 'body' ).addClass( 'adding-menu-items' );
 
+			jQuery('#customize-preview').click(function() {
+				self.close();
+				this.unbind();
+			});
+
 			// Collapse all controls.
 			_( this.currentMenuControl.getMenuItemControls() ).each( function( control ) {
 				control.collapseForm();
@@ -1320,6 +1327,7 @@
 			this.container.find( '.menu-item-handle' ).on( 'click', function( e ) {
 				e.preventDefault();
 				e.stopPropagation();
+				api.Menus.availableMenuItemsPanel.close();
 				var menuControl = control.getMenuControl();
 				if ( menuControl.isReordering || menuControl.isSorting ) {
 					return;