Boss Sir Alex Ferguson told MUTV: "We're going to lose him for the rest of the season. It's unfortunate and it's a bad blow."
Young was at United's 2-2 draw with West Ham on Wednesday night but turned up on crutches.
Ferguson said: "We thought it'd be maybe two or three weeks but now he's been down to the specialist and that's why you saw him at the game on Wednesday.
"We took him down to a specialist in London and the prognosis was not very good at all. We're going to lose him for the rest of the season."