How long does it take for incision on back of hand to close up?

Incision on hand: You don't say if the incision was sutured or left open. If you have an incision which is not healing it could be infected and you should see your doctor.

Time to heal: Your surgeons cut went through many layers of tissue. Each layer heals at a different rate. While skin heals quickly, the deep tough connective tissue (fascia) takes a lot longer. You should minimize strenuous activity for at least 12 weeks and progress slowly. Remember, even when finally healed, that area will never have more than 80% of its strength return.