The winger picked up the problem during France's 3-0 FIFA World Cup play-off victory over Ukraine on Tuesday, which saw Les Bleus qualify for next year's tournament, and is now set to miss the re-match between last year's UEFA Champions League finalists.
"I’m obviously gutted, because I was desperate to play in the big game in Dortmund," he told Bayern's official website.
"But I’m sure the team can do it without me this time."
Ribery joins an injury list at the Allianz Arena club that also includes Bastian Schweinsteiger, Claudio Pizarro, Xherdan Shaqiri and Holger Badstuber.
The 30-year-old has scored eight goals in 16 appearances in all competitions for Bayern so far this season.
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