The summer signing from Barcelona was included in the Bayern team for the 2-0 win over Nurnberg on Saturday, but was withdrawn after taking a knock.
He will now require surgery and has been ruled out for seven weeks, according to a statement on the Bayern website.
"Thiago picked up the injury during the second half of the game against Nurnberg," read the statement. "He will undergo surgery in Munich on Monday and is expected to be out for seven weeks.
Thiago therefore misses Bayern's games against Freiburg, Hannover, Schalke and Wolfsburg while he will also be absent from the Champions League holders' first European games of the season.
The Spain under-21 international has also been ruled out of their DFB-Pokal second-round tie with Hannover next month.