Fletcher missed the 2-0 derby defeat at West Brom at the weekend after suffering a torn calf in training ahead of the game.
He has only started one game this season - the Carling Cup victory at Northampton.
McCarthy said: "It depends on what type of operation he has as to how long he's out for.
"We always try conservative treatment but they're just going to open him up to see. I think it's only going to be a little clear-up operation so hopefully it will only be four weeks."
Kevin Foley also missed the defeat to West Brom but Ronald Zubar is played for the reserves on Monday, while Dave Edwards and George Elokobi are poised to return to training.
Source: Team Talk
Source: Team Talk