The 32-year-old Spain international, who spent eight years at Liverpool before joining Napoli on loan last season, picked up a calf muscle injury in a friendly game against amateur players on Monday.
"He will not be at the disposal of the team for several weeks," Bayern said in a statement.
Reina has yet to make his first appearance in the Bundesliga, which resumes on Oct. 18 after the international matches break.
Bayern's third-choice keeper Tom Starke will be promoted to the bench during Reina's absence.
(Reporting by Karolos Grohmann; Editing by John O'Brien)
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