Add/Remove current_page_parent class

Replace news with your custom post type and menu-item-000 with the menu item you want to highlight.

function wpdev_nav_classes($classes) {
    // Remove "current_page_parent" class
    $classes = array_diff( $classes, array( 'current_page_parent' ) );

    // If this is the "news" custom post type, highlight the correct menu item
    if ( in_array('menu-item-000', $classes) && get_post_type() === 'news' ) {
        $classes[] = 'current_page_parent';
    }

    return $classes;
}
add_filter('nav_menu_css_class', 'wpdev_nav_classes');

If you have more than one post type, it would be better to use a switch statement. Let me know if that’s the case, and I’ll update the code.