Isco missed El Derbi due to neck and back pain, Real Madrid have confirmed.
Isco has fallen out of favour since Solari replaced Julen Lopetegui, with the Madrid coach appearing to hint the playmaker has not been giving enough effort in training.
"In football, you have to work and put all your talent into everything," Solari said ahead of El Derbi. "You have to do that in training so you are available to play."
Isco earlier hit out at Solari via social media, complaining about his lack of game-time in recent weeks despite forwards Bale and Marco Asensio having been sidelined by injury.
Former Madrid midfielder Ruben de la Red said the club do not wait for anyone and told Isco he must perform to the standards of his team-mates, drawing a response from the 26-year-old.
"I completely agree with De la Red, but when you are not getting the same opportunities as your team-mates, that changes things…" Isco wrote on Twitter on Thursday.
"Despite that, I'm continuing to work hard and battling for the moment when those opportunities arrive! Hala Madrid!!"
Isco has only started five LaLiga matches this season and has not been in Madrid's XI for a league game since Solari took charge.
It is unclear how long his injury will keep him out of action, with Saturday's win at Atletico moving Madrid above their city rivals into second place in LaLiga.
Solari's side travel to Ajax for the first leg of their last-16 Champions League tie on Wednesday, with two more Clasico clashes with Barcelona upcoming.
Madrid drew 1-1 at Camp Nou in Wednesday's first leg of the Copa del Rey semi-final, a game in which Isco was an unused substitute.