The Belgium international originally damaged his wrist in October, but had been playing with a protective cast and delaying an operation due to other injuries within United's squad.
However, United have chosen to address the issue after Fellaini missed the victory over West Ham on Saturday with a back injury.
A United spokesperson confirmed to Perform that Fellaini had undergone surgery, but details regarding the length of his absence remain unclear.
United's decision to resolve Fellaini's problem will have been made easier by the return to fitness of fellow midfielder Darren Fletcher, while Michael Carrick is also thought to be close to a comeback.
‘Pep Guardiola had issues in his personal life – was that partly why he didn’t commit earlier, and why they’ve struggled? Were the club reluctant to buy players, in case he left?’ Former Manchester City defender gives view on difficult campaign
EXCLUSIVE: ‘I photographed Oasis in a street in London just because it shared the name of a Manchester City midfielder and Liam and Noel Gallagher loved it’ Legendary snapper Kevin Cummins on the secret behind his cunning masterplan
