I had this issue with my road bike a few years ago. Certainly, what others have stated (padded gloves, changing position, etc) is correct, but what helped me the most was changing my seat angle. I pointed the nose of my saddle up a degree or so from level to take the weight off my hands, and that was the end of the problem. Now, don't go too much or you'll have numbness in another area! It's a fine line.

Good luck!