Young suffered the problem during the closing stages of Monday's 2-1 derby defeat to Manchester City at Old Trafford and is set to miss the Premier League games against Stoke, West Ham and Aston Villa.
"Ashley is out," said Ferguson. "He took a whack on his ankle. He will maybe miss two weeks."
Meanwhile, United skipper Nemanja Vidic is set to return to training after recovering from a calf injury, while his fellow central defender Jonny Evans should be available to face Stoke on Sunday after overcoming the hamstring strain that has kept him out of the last two games.
Ferguson also expects veteran midfielder Paul Scholes, who has been absent since January 26 with a knee injury, to return to training on Monday.
"It will be a terrific boost to get his football intelligence back in the squad," said Ferguson.
"He has been out for a few weeks so we need to get him back out training with us."