The Manchester City midfielder has been confined to the sidelines after hurting his knee during Wednesday's Capital One Cup defeat by Newcastle at the Etihad.
Silva was injured after just nine minutes of the match after tangling with visiting defender Ryan Taylor.
City tweeted the news of Silva's absence: "Manuel Pellegrini confirms he will miss Sunday's game. Will be out for 3-4 weeks."
Manager Pellegrini, speaking at Friday's pre-derby press conference, has challenged his players to step up and fill the void created by the absence of their playmaker.
He said: "David has a problem in his ligament. Maybe he will be out around three weeks, so he will not be available for the derby.
"He is a very important player but I always say the same thing, we have a squad and we have to replace him with another player.
"I think we are a team, and in that team we need top players in top performance always, because that is the best way to play."
The Chilean admits he is also monitoring the situation with Ivory Coast midfielder Yaya Toure but is confident he will be fit to face Louis van Gaal's side.
"Yaya has a small problem but he should play," he added. "We will see him tomorrow but I think he will not have any problems."
City go into Sunday's match on the back of two successive defeats, against West Ham United in the League and Newcastle.
"We need to play faster than we are doing but in both games, against West Ham and Newcastle, the best player of the other team was the goalkeeper," the City boss said.
"I think they know perfectly what we are doing and I am absolutely sure we are going to return to our normal performance.
"If I go (back) one year, it was exactly the same. Around the end of October, we had the same questions, and I answered the same way.
"It is the way we must play. We will continue doing the same way."