Silva was forced off late in Monday's 2-1 derby win over Manchester United and manager Roberto Mancini fears the Spaniard will not recover in time to face Chelsea at Wembley.
Roberto Mancini: "I think it is a hamstring injury. Maybe it is not so bad but I don't think he will be ready for Chelsea.
"Chelsea are in a good moment, they play well and it will be difficult.
"It will be a good game, probably, but it will be different. Semi-finals are different from championship games.
"We are happy because we played very well against United.
"This is the most important thing for us. We deserved to win.
"The game before against United we dominated that game and we lost in the end which I don't know how it's possible but this is football."