Is there a function to cause empty categories not to show in menus?

add_filter( 'wp_get_nav_menu_items', 'nav_remove_empty_category_menu_item', 10, 3 );
function nav_remove_empty_category_menu_item ( $items, $menu, $args ) {
    global $wpdb;
    $nopost = $wpdb->get_col( "SELECT term_taxonomy_id FROM $wpdb->term_taxonomy WHERE count = 0" );
    foreach ( $items as $key => $item ) {
        if ( ( 'taxonomy' == $item->type ) && ( in_array( $item->object_id, $nopost ) ) ) {
            unset( $items[$key] );
        }
    }
    return $items;
}

Please use the above code, it will unset the category which has No post.
Assuming that you were are managing Menu from Apperance->Menu.

Hope that helps 🙂