I think an important factor if it's your plucking hand that hurts is to use your amp. Queg notes above to make sure you're happy with your stage sound. I'd also add to make use of any headroom your amp is capable of supplying. Is easy to do, but resist the temptation to dig in if you can't hear yourself or can't be heard, turn the amp up a simdge instead and play lightly.
Also, the thing is with playing gigs compared to rehearsal is your probably playing a couple of sets of an hour straight with about 10 or 20 secs between each song. In rehearsal you probably pause a good 5 mins between songs to talk about them and experiment with sounds and setup.
So there is a question of fatigue. Yes, strength isn't the be all and end all, but building dexterity will help. So I would advise warming up before playing live, both hands and body. Do some body stretches and hand exercises. A Finger exerciser like the gripmaster is handy to keep in your gigbag as a warm up tool if you can't physically play your bass before you get on stage for some reason. But don't use it to build muscle and strength, it's for flexibility.
The problem with these devices though is they only exercise the closing movement of the hand, not the opening movement required in bass playing. I've seen some people put a rubber band around their fingers and stretch it by opening their fingers to put some tension of the tendons that open the hand. If you get pain on the back of your hand, this may help.
The other one I use for wrist dexterity (keep your minds clean) is the Powerball:
http://www.powerballs.com/
I don't want to sound like a salesman, but this has really helped me. It's funny that right handed players do most of the work with our left arm elevated in the air, which is also our weaker arm. 10mins on the powerball everyday really helps exercise the hands, wrist, arms, shoulder. I couldn't believe how weaker my left arm is to my right. Yes it can be used to build strength if you go fast, but go slower and the gentle action and aid your dexterity.
People may stick their noses up at these suggestions of exercisers and toys as gimmicks and say there's no substitute for practice with a real bass, but so what. If it works, it works.