Without knowing your theme, you have at least a few options. You could 1. hide it with CSS.
.your-page-template-php #your-menu {
display: none;
}
Or 2. you could create a custom header file. For example, duplicated header.php to header-nomenu.php. And in your new file delete the menu. And then in your page template instead of calling
get_header();
you'd call
get_header('nomenu');
EDIT
Upon further review there is a filter inside the wp_nav_menu
function. Conditional logic will probably work as long as you haven't messed around with the query object and forgot to reset it.
function wpa76334_filter_nav_menu($menu, $args){
if( is_page_template('your-template.php')) $menu = null;
return $menu;
}
add_filter('wp_nav_menu','wpa76334_filter_nav_menu', 10, 2);