The Spain international, who had played in all but one of their 15 matches in all competitions this season, had to go off in the 75th minute after tearing a ligament and suffering further damage in his right ankle following a foul.
"Bayern will be without Thiago for several weeks," the club said in a statement after the player's medical examination.
Thiago joins injured world champion Corentin Tolisso and Kingsley Coman on the sidelines, with the German champions having a busy schedule in the coming weeks.
Bayern, second in the Bundesliga, take on AEK Athens in the Champions League next week before facing current German league leaders Borussia Dortmund a few days later.
(Reporting by Karolos Grohmann; editing by Martyn Herman)
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