When the £27.5million Belgian was struck down by a back complaint last month, Moyes opted to send the midfielder away for long-awaited surgery.
It was a further setback for Fellaini, who has struggled to make an impact since his summer move from Everton, and is yet to find the net for his new club.
Even Fellaini's present absence has attracted criticism, with some fans questioning why the 26-year-old could not have played on with a light cast on his wrist.
Moyes has said such a prospect was a non-starter.
"Fellaini will have the cast taken off his hand on Monday," Moyes told MUTV.
"It was a serious wrist injury which needed a major operation.
"It was bad. He had to make sure he got it sorted properly otherwise it might have affected him for the rest of his life.
"He has been able to do lots of running and lots of training but nothing with a football.
"Hopefully next week we will get him back."