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.”
And manager Pellegrini, speaking at Friday's pre-derby press conference, said: “He has a problem with a ligament. He’s a very important player but we have a squad and have to replace him.”
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.
City go into Sunday’s match on the back of two successive defeats, against West Ham United in the League and Newcastle.