Yes it's possible to break your wrist from punching something.
However to actually break your wrist from punching something you would have to punch something such as a wall really hard.
If you punch something that hard then you're gonna be in some serious pain at least for awhile.
Now if you happen to punch someone then it's unlikely you would break your wrist doing that.
You would most likely break someone else's bones before you broke your own bones.
A broken wrist is gonna need some medical attention to repair so if you do or did break your wrist you should go to the doctor or emergency room to get it treated.