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.
"I think it is a hamstring injury. Maybe it is not so bad but I don't think he will be ready for Chelsea," said the Italian.
Mancini admits City will need to produce another battling display against the Blues, who have lost only one of their last five games.
"Chelsea are in a good moment, they play well and it will be difficult," he said.
"It will be a good game, probably, but it will be different. Semi-finals are different from championship games."
Mancini felt that City were good value for their 2-1 victory over United, but insisted the title race was still over after the gap between the sides was reduced to 12 points.
"We are happy because we played very well," Mancini said. "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.
When asked about the title, Mancini replied: "It's finished.
"What is important is only for the second position. [If we finish] 15, 12, 18 points behind it doesn't change anything. I think that we are like them but they score more than us and this is the difference."