Is it possible to make iPod touch undetectable by a router?

Yes, it is possible to make an iPod touch undetectable by a router by disabling its Wi-Fi feature, which prevents it from connecting to or being visible on any network. Additionally, you could put the device in Airplane Mode, which disables all wireless communications. However, if the device is connected to a network, it may be detected by the router, depending on the network's configuration.