Germany international Weigl, who suffered the injury in May, will miss the national team's World Cup qualifying matches in early September, but could be back in action for his club by Sept. 9 when they travel to Freiburg.
The 21-year-old versatile midfielder, who missed Germany's Confederations Cup victory in July, completed much of the training session on Tuesday.
Dortmund won their Bundesliga opener against VfL Wolfsburg last Saturday and after finishing third last season, with Weigl playing in 30 matches, have qualified for the Champions League group stage.
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(Reporting by Karolos Grohmann; Editing by Christian Radnedge)
