The loss of the 24-year-old for the visit of Eduardo Berizzo's side, level with Madrid on 28 points in La Liga, is a bitter blow for Zidane, who will be without suspended trio Sergio Ramos, Dani Carvajal and Casemiro, with Jesus Vallejo injured.
"He hurt himself and we will see. Tomorrow [Thursday] they will do a scan. The player is optimistic but he will not be available on Saturday, that's for sure," said Zidane, before admitting midfielder Marcos Llorente may have to slot into the back four.
"It could happen. He already knows that position. He played it for Castilla some times."
Following their clash with Sevilla, Los Blancos travel to the Middle East for the Club World Cup before returning to take on Barcelona in El Clasico.
With so many important games approaching, Ramos is concerned by the number of his team-mates being suffering from physical ailments.
"[Varane's injury] is the only bad news from the game, another injury," he told beIN SPORTS.
"This season we are getting too many [injuries]. The season is long and it is preferable to have everyone available for the next game."
Madrid raced into a 2-0 lead thanks to goals from Borja Mayoral and Cristiano Ronaldo, before Lucas Vazquez volleyed in the winner after Pierre-Emerick Aubameyang's double got Dortmund back on level terms.
"It was an intense game. We came out with a very strong intensity in the first half-hour," said Ramos.
"Then we lowered our level and they knew how to take advantage of the few chances they had.
"We kept going and we earned the victory to finish the group phase."
Asked for his preferred opponent in the last 16, Ramos added: "None. You have to beat the best to be a champion. The draw is a matter of luck."