The 18-year-old, who has attracted interest from Premiership side Aston Villa, picked up the injury at the tail end of last season and a period of rest failed to cure the problem.
Clarke broke down as he stepped up his workload during training, and the club`s medical team decided an operation was the best course of action.
A statement released by the club read: "Everything was fine with the operation and there were no complications at all, but we can't say exactly when Nathan will return, it could be months."
