The Germany midfielder is absent for the tricky trip to Anoeta having not trained with the team ahead of the encounter after picking up a knock.
Head coach Zinedine Zidane, who also stated that centre-back Jesus Vallejo is unavailable, has seen his squad beset by injuries and suspensions.
Cristiano Ronaldo and Marcelo are banned for the fixture, while Karim Benzema (hamstring) and Mateo Kovacic (adductor tear) are injured.
"I cannot count on them, when you do not train the day before you cannot be involved," said Zidane regarding Kroos and Vallejo's injuries.
"We will not risk it. We hope it's not going to be serious, so we're not going to be silly."
The absence of Kroos may present an opportunity for close-season signing Dani Ceballos, who has been restricted to just two substitute appearances in all competitions this season and has not yet played in La Liga for Los Blancos.
"Dani's going to be with us, he'll be in the squad," added Zidane. "All the players need to have patience.
"For me it's very important, each one of them will have their chance to play I am sure of that.
"With regards Dani, I'm sure that he's ready to play, but these things take time.
"He's training well, he's with the squad and he'll have the chance to play, the chance to start at some stage."
Madrid have made an unbeaten start to the campaign in all competitions, but have drawn their last two top-flight games.