The Frenchman picked up an ankle injury in Saturday's 1-1 draw with Leeds after a heavy challenge from Alan Smith.
Silvestre is now set to miss both legs of the tie with Porto as well as the Premiership games with Fulham and Manchester City and the FA Cup sixth round meeting with either Fulham or West Ham.
United boss Sir Alex Ferguson admitted it was a major blow to lose the influential French international with Rio Ferdinand already missing through suspension.
"Mikael will be out for three weeks," Ferguson told the Manchester Evening News.
"It is a big blow for us but we will just have to get on with it."
In Silvestre's absence Roy Keane is set to drop back to defence to partner Wes Brown in central defence.
Ferguson has backed Brown to come good after an indifferent return to action following a long-term injury.
"I am not interested in what other people think," added Ferguson. "Wes will be back.
"I know what we know. The boy needs games and good training.
"Nine months out of the game is a long time, particularly as he has had three major injuries in his career and has only just turned 24.
"He has missed almost three years of football at this club which is a lot.
"There have been genuine signs that he is getting there and in a couple of games he will be back to his best."
