The 25-year-old Turkey midfielder, who returned to Dortmund in 2013 following unsuccessful spells at Liverpool and Real Madrid, had inflamed tissue removed from his left knee.
"Borussia Dortmund team doctor Markus Braun expects his recovery period to last about two months," Dortmund said in a statement.
Dortmund, last season's league runners-up, are also competing in the Champions League Group D along with Arsenal, Galatasaray and Anderlecht.
The German-born Sahin joins several other Dortmund players, such as Ilkay Guendogan, who has not played since last year, Jakub Blaszczykowski and Marcel Schmelzer on the sidelines.
(Reporting by Karolos Grohmann; editing by Amlan Chakraborty)
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