The winger had the operation last Thursday, with tests on Monday showing the procedure had been successful in removing bruising that had been affecting a nerve.
The holders confirmed that the 30-year-old would return to training next week and will miss the first leg of their last-16 Champions League meeting at the Emirates Stadium on 19 February.
A statement on Bayern’s website said: “An examination on Monday revealed that the bruise, which had pressed on a nerve, was completely removed by surgery. Ribéry is scheduled to begin exercise therapy later this week and, a week later, he will return to running training.
“Therefore Ribéry will miss the next games for the champions, among them the last-16 tie at Arsenal.”
Ribéry is Bayern’s most influential player and made the three-man shortlist for the Ballon d’Or earlier this year.
