hello - well there could be a couple of things causing this:
a) your bike fit. Did you get professionally fit to your bike? Very important
b) avoid holding all your weight on your hands and wrists (make sure the nose of your seat isn't slanted forward)
c) you may need a little more cushion on your bars. Try gel bar tape or tape that adds additional padding to reduce the vibration.
d) are your gloves well cushioned? There are all types of gloves out there, some have more padding than others. You may need to get a set with more padding.
Good luck!