"We've had a bad blow with Darren and it emphasises the futility of playing these friendly games," said Ferguson.
"He should have played for 45 or 60 minutes at most, but he played the full game so he's out for six weeks."
Fletcher was left out of United's squad for the 3-0 win over Liverpool last weekend, but recovered sufficiently to play in George Burley's first game in charge of Scotland.
"He was recovering from a bad chest cold and we rested him last Sunday because of that," added Ferguson.
"It's a bad blow for us and it's crazy. Supporters will stop going to these kind of games.
"They have the whole of the end of May, too. (England) have fixtures against Trinidad and the USA and I think every manager knows that they're a waste of time."