Spain international Thiago, who has been with the German champions since 2013 when joining from Barcelona, picked up an injury playing for his country in the 3-0 World Cup qualifying win over Albania last week.
The 26-year-old, who will sit out the final group match against Israel on Monday, was sent for an MRI scan and the results have confirmed he has suffered a strain to his ankle ligaments.
He is now expected to miss a handful of training sessions ahead of the return to domestic action this weekend and Bayern, who are second in the Bundesliga, are confident the midfielder will be available for the clash against Freiburg at the Allianz Arena.
"Thiago has strained an interior ligament in his ankle and must only take a short break from training," the club said in a statement. "The 26-year-old will in all probability be back for the home game against Freiburg."