Reus, who has 17 goals for Dortmund in all competitions and is the club's leading scorer, injured his thigh during their German Cup defeat by Werder Bremen last week and missed their draw with Hoffenheim in the league at the weekend.
"We would, of course, have liked to have him in London, because his presence is a bit intimidating for the opponent," Dortmund official Sebastian Kehl told reporters. "But we'll compensate for his absence."
Jadon Sancho, the 18-year-old English winger who has eight goals and 10 assists in all competitions, is expected to take Reus' place in the starting lineup.
It is unclear whether Reus will be fit for the return leg on March 5.
(Reporting by Rohith Nair in Bengaluru; Editing by Peter Rutherford)