The summer signing has played on with the injury in recent months, knowing that an operation was inevitable, but has been on the sidelines for three weeks with a back problem. So the decision was taken to send the Belgian for wrist surgery.
"He had his operation on Saturday morning," Moyes said at the Aon Training Complex on Monday. "We couldn't get him recovered from his back injury. We thought his back would be okay after 10 days but it wasn't getting better, so we made a quick decision to get his wrist operated on.
"We think it will be six weeks but there's a chance it will be before that. His back problem was just going to take time. It was a muscle injury, which wasn't healing so it was going to take longer than expected. That's why we decided to get the wrist done."
Fellaini has been unlucky with injuries as he acclimatises to life at Old Trafford. "He doesn't feel 100 per cent fit because of the wrist," Moyes added. "He got the back injury against Everton and since then he's not been right, but we thought we might have got him back in a couple of weeks. "He tried it and it wasn't right, so we thought the best idea was to move on, have the surgery on his wrist and give his back a chance to get well too."
More positively, Robin van Persie (thigh) and Michael Carrick (Achilles) could return over the festive period. "There are always miracles at Christmas so let's hope there could be one for Robin or Michael Carrick."