The France international had surgery on the unusual injury on Thursday and will stay in hospital until Sunday with no date for his return yet set.
“I hope that he can return to training with us as soon as possible,” Bayern coach Pep Guardiola said in a club statement on Friday.
Bayern, 13 points clear at the top of the Bundesliga after 19 matches, visit Arsenal in their Champions League last 16 first leg on February 19.
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