The injury has annoyed United boss Sir Alex Ferguson who thought that Fletcher would only play for a a maximum of one hour of the game at Hampden Park.
"We've had a bad blow with Darren and it emphasises the futility of playing these friendly games," the United boss has said.
"He should have played for 45 or 60 minutes at most, but he played the full game and now he's out for six weeks.
"He was recovering from a bad chest cold and we rested him last Sunday because of that."