Germany international Bender stretched ankle ligaments in Saturday's 1-0 defeat to Bayer Leverkusen and he joins a long list of key absentees including Ilkay Guendogan, Mats Hummels and Neven Subotic.
Playmaker Nuri Sahin, who partly tore an ankle ligament in the same game, has a chance of being fit, the club said in a statement.
Last season's runners-up need to win their final Group F game at already-eliminated Marseille to guarantee a place in the knockout stage.
Arsenal top the group on 12 points with Dortmund second on nine points, the same as Napoli.
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