The Spain international underwent surgery in Barcelona on Tuesday, joining fellow central defender Jerorme Boateng, out for three months, on the sidelines at Bayern.
"Thank you all for caring. Fortunately it is not a serious injury," Martinez said on Twitter.
Bayern, chasing a treble of titles in coach Pep Guardiola's last season at the club, are struggling with their central defenders, with Medhi Benatia also out and still working on his comeback from injury.
The German champions signed central defender Serdar Tasci on loan from Spartak Moscow on Monday in an effort to plug the gaps left by the injured players.
Bayern are top of the Bundesliga with an eight-point lead and are also in the running for the Champions League, where they face Juventus in the round of 16 later this month, and the German Cup.
(Reporting by Karolos Grohmann; editing by Justin Palmer)
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