Which hand? Fretting or struming?
Are they sure there's been no displacement? Even a little?
I'm saying this because I broke my wrist about a year and a half ago. Fretting hand. What the doctor thought was fine was not fine for the extreme movements required for fretting. I can still play but some movements are hard/impossible. I should have had surgery when it happened to bring it to normal and I'm too old now to go through the hassle so I live with it. Tell your doctor what's important to you and find out if your break will still allow that once healed.
ETA: I see it's your fretting hand. Make sure everything will heal back the way it was.