According to the Bavarians' official website, the 22-year-old defender has suffered a hairline fracture on his left foot, meaning he has now joined Rafinha and David Alaba on the sidelines.
Contento has now been instructed by club doctors to rest for 10 days before a final decision is made on the appropriate course of treatment.
The versatile Alaba, who can also play in midfield, suffered a stress fracture in Bayern's friendly defeat by Napoli last month and it was ultimately decided that surgery was the best route to go.
Meanwhile, Rafinha tore ankle ligaments in the same game but does not require an operation.
Jupp Heynckes is now likely to be without three recognised full-backs for their DFL-Supercup match against Borussia Dortmund on August 12.
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