Add a shortcode to a specific menu item

wordpress-menu-filter.php

<?php
/**
 * Filters all menu item URLs for a #placeholder#.
 *
 * @param WP_Post[] $menu_items All of the nave menu items, sorted for display.
 *
 * @return WP_Post[] The menu items with any placeholders properly filled in.
 */

function iv_dynamic_menu_items( $menu_items ) {

	foreach ( $menu_items as $menu_item ) {
		if ( '#profile_link#' === $menu_item->url ) {
			global $shortcode_tags;

			$shortcode = 'my_shortcode';

			if ( isset( $shortcode_tags[ $shortcode ] ) ) {

				$atts    = array();
				$content = '';

				$menu_item->url = call_user_func(
					$shortcode_tags[ $shortcode ],
					$atts,
					$content,
					$shortcode
				);
			}
		}
	}

	return $menu_items;
}
add_filter( 'wp_nav_menu_objects', 'iv_dynamic_menu_items' );