You're not the first golfer to experience this problem. The wrist bone commonly broken from a ground-slamming divot is the hamate bone. It is near the wrist on the pinky side of the palm of the hand.
The hamate bone forms one side of Guyon's canal, the small passageway that surrounds the ulnar nerve as it travels into the hand. In the hand, the ulnar nerve goes to the ring and pinky fingers, the small muscles in the palm of the hand, and the muscle that pulls the thumb into the palm of the hand.
A fractured hamate bone in the wrist can pinch the ulnar nerve inside Guyon's canal and produce symptoms of weakness as you've described. Be sure to let your doctor know about these symptoms.