The answer depends hugely on what router you're using.
If the router has an RS-232-type connector (a D-sub, or an RJ-45 on a Cisco), you need something like a MAX232 to interface to the Arduino. However, the router's serial interface is probably not available for any purpose other than hooking up a terminal or emulator as a console.
If you're using something like a WRT54G that's been hacked with DD-WRT, where you have to solder wires to the route's PC board, it might be usable as a non-console serial interface.