The midfielder is also suffering from a back injury, which prompted David Moyes to sanction the operation.
The midfielder has not featured for the Premier League champions since the club's 1-0 defeat to Everton on Dec. 4.
"Fellaini had a bad twinge in his back and the club think now is the best time to also operate on his wrist," a source close to the club told Goal UK. "United didn't want to do anything with the wrist until the summer but Belgium have been pushing them for three months to sort it out with the World Cup in mind.
Fellaini's Old Trafford career has been hampered by injuries since his 27.5 million pound arrival from Everton in September, and David Moyes said Saturday that the club was concerned by the midfielder's slow recovery.
"Fellaini has an injury to his back, which we hoped might have healed up but it hasn't," Moyes told reporters. "I am going to get another scan and if it hasn't healed up then I might need to take the decision to get his wrist done as well."