Los Blancos' superstar striker did not train on Friday because of an unspecified knock and will not travel to Jose Zorrilla, where Madrid is looking for a fourth straight top-flight win.
Head coach Zinedine Zidane is unsure if Benzema will return for the Round of 16 first-leg tie at Atalanta and said he will be re-evaluated ahead of that game.
"Karim won't be with us tomorrow, he has a little niggle, he has something and he won't be with us tomorrow," Zidane said on Saturday (AEDT).
"We hope he's ready for Wednesday, from Sunday-Monday onwards we'll see how his problems evolve and how he's ready for Wednesday [Thursday AEDT]."
It is an unwelcome blow for Zidane, whose squad has already been ravaged by injury with Benzema joining Eden Hazard, Rodrygo, Federico Valverde, Alvaro Odriozola, Eder Militao, Marcelo, Dani Carvajal and captain Sergio Ramos on the sidelines.
"I think any injury we get is a hammer blow for us. But of course we know the player Karim is for us, how important he is," Zidane added.
"But as I said before he is injured, he won't be available tomorrow and we have to do the best we can.
"We have to think about players who are there and recover Karim as soon as possible. The same goes for all the other players."
Despite its injury woes, Madrid has performed well over the past week in LaLiga and Zidane was asked if he is confident the team can show a similarly positive attitude in Europe.
"It is what it is. Mentally we can't do anything about these injuries. We just want to avoid more injuries," he said.
"I think everyone here is committed to doing that but so many factors go into this. It's true that lately a lot of players are injured and it doesn't help.
"We have so many injuries, today we had another with Benzema but we just need to be patient and the players who are available we just need to give it our all, and just hope we are going to recover our players.
"I know the players want to get back to training and on the pitch. I hope we get all our players back but it's true lately it's become a little complicated, yes."