The Brazilian suffered ankle ligament damage in training at the Allianz Arena on Saturday.
"I'm very disappointed," Rafinha is quoted as saying by his club's official website. "I had a really good preparation, and now this. I am very sad."
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Rafinha was expected to be sold last summer but went on to establish himself as a first-team regular under new coach Pep Guardiola.
The 28-year-old's injury is a major blow for the Bavarians, but the German champions do have the option of restoring Philipp Lahm to his more familiar role of right back, with the World Cup winner having been often utilized as a defensive midfielder during the 2013-14 season.