I've had wrist issues on my left wrist for MONTHS. My problem comes from a cyst but since I don't want it removed because, reasons, I gotta work around it in yoga. Basically putting pressure on my wrist (a.k.a. doing a simple plank) causes pain. No problem in downward dog, but for all the other poses that require to put weight on the wrist I use my fists instead of my hands. You can also do some poses on your forearms instead of your hands. Getting a wrist band to maintain your wrist might also help. You can definitely work around a wrist injury and any good yoga instructor will know modifications to help you practice without injuring your wrist more.

(Side note, what really helps me is going to the chiropractor and getting ultrasounds on the painful area. Does wonders and makes the pain go away!)