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.
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