Man United's Fellaini faces new spell out after surgery
Marouane Fellaini (right) clashes with Real Sociedad's David Zurutuza during the Champions League game at the Anoeta stadium in San Sebastian on November 5, 2013
The £27.5 million (33 million euros, $45 million) summer signing from Everton has been absent since the start of December due to a back problem.
But he has also been hampered by a wrist problem for several weeks and has been playing with a cast.
As Fellaini was struggling to return to action from the back problem, United decided to bring the surgery forward.
The Belgian international, who has struggled for form since his move to Old Trafford, is now likely to be absent until February.
Moyes said: "He had his operation on Saturday morning. We couldn’t get him to recover from his back.
"We thought his back would be okay after 10 days but it wasn't getting any better so we made a quick decision to get his wrist operated on and he has had that done now.
"We think he will probably be out for six weeks but there's a chance it could be shorter. His back problem was a muscle injury that wasn't healing.
"It's unlucky. He doesn't feel 100 percent fit because of his wrist and he was finding it difficult.
"I asked him if he could get over the Christmas period but it wasn't right. There's no doubt he will be a good player for us."
Moyes is also hopeful that striker Robin van Persie and midfielder Michael Carrick can return over the festive period.
Van Persie is struggling with a thigh injury and Carrick has been out for several weeks with an Achilles injury.
"There are always miracles at Christmas so let's hope there's one for Robin van Persie and Michael Carrick," Moyes added.
"This is the time when miracles happen. You just never know."
Moyes has been pleased with the continued good form of Wayne Rooney, but the United manager admits there is no news on a potential new contract for the England striker, whose current deal expires in the summer of 2015.
"As far as I know it's just the same as it was. The club and Wayne's people are speaking regularly.
"He has played behind the striker in all of the games. He's a goalscorer but he can make goals as well. That's part of his job.
"Part of a centre-forward's job is to make goals. He is scoring but also assisting."
The Scotsman has made no secret of his desire to make additions in the January transfer window after Fellaini was the club's only addition in the summer.
But he says there is also potential for the club's loan players to return and have an impact in the second half of the campaign.
Jesse Lingard, Nick Powell and Ryan Tunnicliffe have all impressed during respective loan spells at Championship sides Birmingham City, Wigan Athletic and Ipswich Town.
Moyes said: "We will try in January. I'm quite actively looking at our own boys, the likes of Jesse Lingard, Nick Powell and Ryan Tunnicliffe.
"We have quite a lot of boys on loan and they are the ones I am making sure to keep eyes on. They are the future.
"They are part of the club. They have been in the system and we hope they might be able to come back and help if we need it in January."