The Germany international, 26, was sidelined for their 4-2 win over Hannover in the Bundesliga at the weekend, and has failed to recover in time for their next encounter at Signal Iduna Park.
As a result Reus – who scored a hat-trick in the play-off second-leg thrashing of Odd – will not get the chance to add to his four goals in the competition until later in the group stage.
"Marco Reus is unfortunately not available for tomorrow," Dortmund coach Thomas Tuchel told reporters. "He should be back into full team training on Friday."
Tuchel could turn to Adnan Januzaj to replace Reus after the Manchester United loanee impressed as a substitute on his Dortmund debut against Hannover.
"We are very pleased with Januzaj since he arrived here," he added. "He was immediately part of the group, and his talent is obvious.
"He is an option for tomorrow; he still needs to get used to the intensity, but we trust him to do that very quickly."