I am not really sure whether there is some native function for this or not, but you could do it like this:
$menu_object = wp_get_nav_menu_object("Main menu");
$menu_items = wp_get_nav_menu_items($menu_object->term_id);
$menu_items_count = 0;
foreach ( (array) $menu_items as $key => $menu_item ) {
if ($menu_item->menu_item_parent == 0 ) $menu_items_count++;
}