You can use the remove_submenu_page function to remove updates menu from WordPress admin panel. Here is the snippet:

add_action( 'admin_init', 'wpse_38111' );
function wpse_38111() {
    remove_submenu_page( 'index.php', 'update-core.php' );
}

(ref: http://codex.wordpress.org/Function_Reference/remove_submenu_page)