The midfielder is set to miss two-to-three weeks of action after picking up the problem in his side's defeat to Gladbach
The 25-year-old, who is on loan at Signal Iduna Park from Real Madrid until the end of the season, picked up the injury in the Schwarzgelben's 2-0 loss to Borussia Monchengladbach, which saw them surrender their unbeaten start to the Bundesliga season.
BVB team doctor Markus Braun made the assessment on Sunday which rules the Turkey international out of contention to feature in upcoming World Cup 2014 qualifiers against Estonia and the Netherlands.
Sahin joins club captain Sebastian Kehl and Ilkay Gundogan on the sidelines as Jurgen Klopp's side bad luck continues on the injury front.
Dortmund will be looking to bounce back from their first domestic defeat of the season in their next clash at home to Hannover on October 19.