It depends upon how that LED is wired up. If you're lucky enough that the LED has its cathode wired to ground and you can share a common ground with that circuit, you can just measure the voltage at the LED anode with an analog A/D input. It'll be 0 when the LED is off and quite a bit not 0 when the LED is on (probably in the 2-3V range, but could be as high as 4V or so for white LED's).
If you don't want to connect the circuits together, you can use an optodarlington to draw a bit of current from the LED (like an LTV-815) and switch an Arduino input to ground when the LED turns on (use the Arduino pull-up resistor to keep it high otherwise). You'll need a resistor in series with the optodarlington input to prevent too much current from going to it and making the LED dim. I'd start with 10k and go down as necessary.
The Gadget Shield
: accelerometer, RGB LED, IR transmit/receive, speaker, microphone, light sensor, potentiometer, pushbuttons