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.
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The Gadget Shield: accelerometer, RGB LED, IR transmit/receive, speaker, microphone, light sensor, potentiometer, pushbuttons