Moyes stated the Reds intend to delay the operation while the club doctors decide on the best cause of action.
"Fellaini needs an operation, unfortunately. It's quite a bad wrist injury," the manager told MUTV. "There's a bit of bone and ligament sticking out but we've been told we can get away without operating for now."
The Belgian midfielder's injury threatened to leave United short in the middle of the park with Tom Cleverley also picking up a calf injury, but the boss is confident the club will be able to put off the procedure for as long as possible.
"We can put it off for as long as two years. It's not in desperate need of doing, but it's whether he feels okay to play or not," Moyes stated.
Fellaini is likely to play in the intervening period between his operation, wearing strapping on his hand in order to avoid exacerbating the problem. However, Moyes is wary that a degree of care and attention needs to surround the Belgian's injury if he is to continue playing.
"Obviously you use your arms quite a bit to hold people off in the game and it's important that we make sure his wrist doesn't get any further damage."
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