The Belgium star then underwent surgery to repair damaged tendons over the weekend, possibly ruling him out until the end of February.
Fellaini has been struggling with the wrist injury for some time, although it had been possible for him to play through the discomfort.
Moyes always knew an operation would eventually be necessary, with the player preferring to go under the knife before the World Cup.
However, a separate back injury - which has forced him to miss five games since December 4's outing against his former club Everton and shows no immediate sign of clearing up - has led Moyes to get the wrist sorted.
Fellaini will now miss around 10 games including a home tie against Tottenham and an away clash at Chelsea but it is hoped he will be back for the first leg of the Champions League last 16 encounter with Olympiacos on February 25.
Fellaini has struggled to make an impact since his £27.5million move from Goodison Park on transfer deadline day.
He has so far failed to score for his new club in a series of ineffective performances and on Friday, Moyes highlighted the current injury woe.
"We think probably he will be out for six weeks but there's a chance it could be shorter than that," said the United boss.
Fellaini has also struggled with a back problem this season and Moyes said: "His back problem was just going to take time. He has a muscle injury in his back which wasn't healing.
"That is maybe going to take longer than we expected so that's when we decided to get the wrist done. He's been unlucky.
"He does not feel 100 percent fit because of his wrist so he's found it difficult."