The 22-year-old was initially expected to be fit for Sunday’s league climax, but Sir Alex confirmed the problem is worse than first thought.
Ferdinand is fit to take his place in defence at the Stadium of Light, but Danny Welbeck will not be available, though the striker is expected to be fit for Euro 2012.
"Chris Smalling got a bad injury last week," Sir Alex said at his Friday press conference. "We tried to take him off, then Rio got a knock.
"He’s going to miss the European Championship. At the moment we're assessing what we'll do, but certainly it's a bad injury. I can play Phil Jones back in there with Rio, who is okay."
United are level on points with leaders Manchester City going into the final game, but the Blues have a greatly superior goal difference and will almost certainly win the title if they beat QPR at home. But Sir Alex knows all he can do is focus on United’s game.
"Everyone wants to win the last game of season and we're no different," he said. "We'll do our best and hopefully something stupid will happen to City."