The Belgium star has been playing with a protective cast on his hand during the recent internationals and Moyes is keen for him to continue playing for United, particularly with Tom Cleverley ruled out by injury.
"Fellaini needs an operation," said Moyes. "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 is likely to feature against Southampton this weekend, but one man who is a doubt is striker Robin van Persie.
Van Persie picked up a knock to his calf on international duty with Holland on Tuesday.
"We have a few with knocks," Moyes told MUTV. "The one we are more worried about is Robin van Persie.
"He got a kick on the calf and he came off in the second game (against Turkey). He has had problems with his toes as well."
Van Persie's hat-trick against Hungary last Friday took him top of the Dutch international scoring charts.
"It is an incredible achievement," said Moyes. "What he wants to do now is score more goals for Holland and do it in a World Cup when it matters.
"But there have been some brilliant Dutch forwards over the years and they have had an array of talent. To be at the top of that list is something special."