A perfect start to the Bundesliga campaign continued for Dortmund with a 3-1 victory, but the win came at a cost as Hazard left the field five minutes from full time after colliding with an opponent.
The Belgium international, who arrived at Signal Iduna Park from Borussia Monchengladbach in May for a reported €25.5million, is now facing a spell on the sidelines and is unlikely to play a part in his national side's upcoming EURO 2020 qualifiers with San Marino and Scotland.
Dortmund announced the news of his lay-off on its website.
Hazard started Dortmund's first two league games of the season and also played 88 minutes in the DFB-Pokal win at Uerdingen.
Lucien Favre's side faces Union Berlin on Saturday and then have a two-week break before its next outing at home to Bayer Leverkusen.