Bayern announced the France winger would definitely miss Saturday's Bundesliga clash with Nurnberg after having a "minor operation" to repair a burst blood vessel in his buttock.
The club said in a statement on their official website that surgery became necessary at short notice because bruising associated with the damage was affecting a nerve.
Ribery, Bayern's most influential player who made the three-man shortlist for the Ballon D'Or, will remain in hospital until Sunday and will undergo a post-operative examination the following day.
It is not yet known how exactly long the player will be out for.
"I hope he can train with us again as soon as possible," Pep Guardiola said.
Arsenal face defending champions Bayern in the first leg of their last 16 tie in London on February 19.