The club's manager told reporters: "Fellaini needs an operation. It is quite a bad wrist injury. There is a bit of bone and ligament sticking out.
"We have been told we can get away without operating just now and we are a little bit short with Tom Cleverley picking up a calf strain for England, so we need him and we will put it off as long as we can.
"That could be as long as two years. It is not desperate but part of it is does he feel OK to play. You do use your arms to hold people off and we have to make sure his wrist is not suffering any more damage than it is already."
Fellaini will be available to play against Southampton this weekend.