Index: src/wp-admin/js/customize-nav-menus.js
===================================================================
--- src/wp-admin/js/customize-nav-menus.js	(revision 34770)
+++ src/wp-admin/js/customize-nav-menus.js	(working copy)
@@ -1132,6 +1132,10 @@
 					}
 				});
 				if ( settingValue ) {
+					if ( property === 'classes' && _.isArray( settingValue[ property ] ) ) {
+						settingValue[ property ] = settingValue[ property ].join( " " );
+					}
+
 					element.set( settingValue[ property ] );
 				}
 			});