I recently had a hysterectomy, during the suture removal it broke and a piece was left inside. What should I do? Will it come out by itself?

Retained sutures. Occur frequently and it should be of no consequence. Permanent sutures are used internally in many situations to prove this point. But if the suture does ever show itself and it doesn't easily come out, see your doctor to have it removed.
The . The short answer is you should go back to your doctor and have it removed properly. There is a chance it may come out by itself, but it's best not to wait around to see if that happens. The reason being, the longer it stays in, the greater the chance of infection. Good luck.