The 26-year old Spaniard has already been ruled out of Tuesday's Champions League clash with Borussia Dortmund and is a major doubt for the home meeting with the league leaders.
"It's a hamstring. We don't know if he can recover for the derby. We will try," said manager Roberto Mancini.
The potential loss of Silva for the Dortmund fixture could add to the absence of midfielder Yaya Toure who will miss because of suspension and creates some uncertainty ahead of the top-of-the-table Premier League clash on Sunday.