Schmelzer, 23, will miss Saturday's Bundesliga match against Mainz, and also next week's Champions League match at Marseille.
"He will be doing rehabilitation work until Monday and then can return to team training. So playing in Marseille on Sept. 28 is unrealistic," Dortmund posted on its website.
Dortmund tied Arsenal, 1-1, in its first Champions League match, but has three losses through six matches in the Bundesliga. The defending Bundesliga winners had just five losses last season.