Losing the Spain playmaker for a game which could have a significant bearing on the Premier League title race would be a major setback for Roberto Mancini, City's manager.
"It's a hamstring. We don't know if he can recover for the derby. We will try," said the Italian.
Silva, 26, who provided more assists than any other player in the division last season, has already missed key games after suffering a hamstring injury on international duty with Spain in October.
Manchester City striker Edin Dzeko hopes the team can shrug off the absence of key players to salvage something from their dismal European campaign and Sunday's Derby.
City cannot reach the Champions League knockout stages and have just a consolation spot in the Europa League to aim for as they head into their final Group D game against Borussia Dortmund.
The English champions need to win in Germany to have any chance of achieving even that and they must do so without Yaya Toure and Silva.
Toure is taking an enforced break through suspension.
Midfielder James Milner and left-backs Gael Clichy and Aleksandar Kolarov are also injured for the clash at the Westfalenstadion.
Dzeko said: "We still have a chance to play in the Europa League.
"We will do our best to try to win because only if we win can we continue in the Europa League.
"It won't be easy and we have a few players missing but we will do our best because everything is possible in football.
"In the Champions League we didn't play like we wanted, I think in the Premier League we are playing very good.
"We haven't lost any games and I hope we will continue like that.
"If we can play in the Europa League that would be good for us."