The Portuguese superstar went under the knife in Amsterdam on Monday in an attempt to resolve a protracted problem.
The operation was performed by Professor C. Niek van Dijk at the Academic Medical Centre in the Dutch capital.
The Red Devils released a statement to say early indications are that the procedure went according to plan, although no time scale has been set for a return to training.
It is hoped that a review by the specialist in one month's time will allow an estimation to be made on a possible return date.
However, for now the 23-year-old will begin his recovery under the watchful eyes of the United medical staff.