The 22-year-old, who cost Bayern 25 million euros (US$33.45m) from Barcelona in July, limped out of Bayern's 2-0 win over Nuremberg on Saturday.
A scan by Bayern's team doctor Hans-Wilhelm Mueller-Wohlfahrt confirmed the need for an operation on his right ankle and recuperation for up to seven weeks.
The attacking midfielder is expected to miss half of Bayern's Champions League group stage matches, as well as Spain's internationals against Finland and Chile next month.
Bayern have won all three of their opening Bundesliga games so far, but are third in the table behind leaders Borussia Dortmund and Bayer Leverkusen.
Bayern Munich's star Thiago Alcantara faces upto seven weeks lay-off
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