The French international underwent a "minor operation" to repair a burst blood vessel in his buttock last Thursday, with tests on Monday showing the procedure had been successful in removing bruising which had been affecting a nerve.
However, Bayern also confirmed that the 30-year-old would only return to training next week and will miss the first leg of their last-16 Champions League meeting with Arsenal in London on 19 February.
A statement on Bayern's official website said: "An examination on Monday revealed that the bruise, which had pressed on a nerve, was completely removed by surgery last Thursday.
"After healing, the 30-year-old is scheduled to begin exercise therapy later this week and, a week later, he will return to running training.
"Therefore Ribery will miss the next games for the record champions, among them the last-16 tie at Arsenal in the Champions League."
Ribery is Bayern's most influential player and made the three-man shortlist for the FIFA Ballon d'Or earlier this year.