The promising 19-year-old striker - who made his first team debut against Blackburn in December 2011 - sustained the blow while in action for England's under-19s side on Wednesday evening.
Keane had to be substituted after turning awkwardly during his side's victory over Switzerland, and a subsequent scan has confirmed the severity of the injury.
Speaking to ManUtd.com, Sir Alex said: "I'm very, very disappointed for the lad. He was in the first-team squad for next season."
It is not yet known how long Will's rehabilitation period will take, but Nemanja Vidic - who suffered the same injury last December - is aiming to return in time for the start of the 2012/13 campaign.