The Spain international suffered another blow when he sustained a partial tear of the medial collateral ligament in his right knee in training last week.
Thiago has been plagued by injuries since his move from Barcelona 15 months ago and Bayern coach Pep Guardiola admitted the Bundesliga champions may have made a mistake in the manner in which they managed his previous knee problem.
The Bavarian giants revealed on Thursday that the 23-year-old has gone under the knife and the operation went according to plan.
A club statement said: "The operation in Barcelona, attended by FCB team doctor Dr Lutz Hansel, was completed without any complications.
"However, Thiago faces a long layoff and is likely to be out of action for several months."
Free-scoring Bayern face Borussia Monchengladbach in the Bundesliga on Sunday, when they will be eyeing a seventh consecutive victory in all competitions.
