The 28-year-old defender, who had played in every competitive match for the German champions this season, was injured in their 1-1 Bundesliga draw against Cologne on Saturday.
"He has been ruled out for the near future... and also called off his participation with the Spanish national team for their upcoming qualifiers in Italy and Albania," Bayern said in a statement.
Spain, top of Group G on three points after one match, travel to Turin on Oct. 6 before taking on Albania in Shkoder three days later.
Bayern are top of the Bundesliga with as three-point lead having won five of their opening six games.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
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