Manager Manuel Pellegrini revealed the duo will miss out after failing to recover in time for the visit of Roberto Martinez's side.
Jovetic, who scored his fourth league goal of the season against Sunderland on Wednesday, picked up a knock early in the second half and was replaced by James Milner after 56 minutes.
Silva (knee) has not featured for City since their 2-0 defeat to Newcastle United in the League Cup in October, and Pellegrini revealed the Spaniard faces a race against time to make their crucial UEFA Champions League clash with Roma next week.
Captain Vincent Kompany (hamstring) will be unavailable to face Everton, but Aleksandr Kolarov and Edin Dzeko (both calf) are ready to return.
"Kolarov and Dzeko are in the squad [to face Everton]," said the Chilean. "[But] Silva and Jovetic are out.
"We have a last test on him [Kompany] on Monday to decide [if he can face Roma]. It is possible he could travel."
Pellegrini expects a tough test from Everton on Saturday, but believes City have found their stride again and can extend their five-match unbeaten run in all competitions.
"They [Everton] like to have possession and have very technical players," he added. "I am sure against us they will be a very strong team.
"[But] we're returning to our normal performance. Important players are playing well and that means the team play well."
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