Toprak, who made his comeback from a three-week break in the 1-0 win over Hamburg SV on Sunday, was injured late in the game.
The 26-year-old Turkey international also missed the 2-0 first-leg loss to the Spaniards.
"He will now miss the team's upcoming games against Villarreal on Thursday and the one against VfB Stuttgart in the Bundesliga on Sunday," the club said in a statement.
Leverkusen are seventh in the league, battling for a top- four finish and a place in the Champions League next season.
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(Reporting by Karolos Grohmann, editing by Ed Osmond)
