I get similar pain when my wrist are under pressure in the extended position. I saw a Dr. and he told me it was a ganglion cyst, so other than surgery (or not doing anything, which isn't an option) the only thing you can do is tape or wrap.
I've had to modify how I lift: I can't put any pressure on my wrist, so I use DBs instead of barbells for bench, pushups on the knuckles instead of palms, and I can't do cleans or front squats correctly so I do snatch and OH squats.
If your wrist is sore for long periods of time, your range of motion is limited and it hurts to press on the back of your had, where the tendons cross the wrist bones, you may have a ganglion cyst. Get it checked by a Dr. to be sure, but like someone suggested, use wraps or tape to prevent extension.