The Armenian midfielder played the final 25 minutes of Dortmund's 2-0 loss at the Coface Arena - replacing Shinji Kagawa midway through the second half.
Mkhitaryan was involved in a collision when shooting at goal late in the game and underwent diagnosis on Saturday following the team's return to Dortmund.
The club confirmed on Sunday that the 25-year-old is likely to be sidelined for four weeks of action and could therefore miss up to six games - including two UEFA Champions League fixtures and next week's Ruhr derby against Schalke.
Mkhitaryan joins a lengthy injury list for Dortmund coach Jurgen Klopp, with Marco Reus, Jakub Blaszczykowski, Ilkay Gundogan, Nuri Sahin and Oliver Kirch also currently out.
Mkhitaryan, who arrived from Shakhtar Donetsk in 2013, scored 13 goals in all competitions in his debut campaign last term.
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