The 19-year-old, who remains in limbo over his future, sustained the problem during a reserve match earlier this week.
"Paul got injured in Monday and he is out for the season," Ferguson said in a press conference.
Meanwhile, Ferguson stated that Michael Owen could return to the side next week as the striker nears a recovery from injury.
"I have said time and time again that Michael is a player who can score important goals if you are struggling in a match," Ferguson added. "He has had a hard time with injuries. When he gets them it is usually months."
The Red Devils will try to stretch their lead at the top of the table to eight points when they take on Everton on Sunday.