The former France international has been at the Allianz Arena since 2007, winning 18 trophies during his nine-year stay in Bavaria, although injuries have restricted his first-team appearances in recent seasons.
The 33-year-old's previous deal had been due to expire at the end of this season, but he has now penned a new contract that will run for a further 12 months.
Ribery, who was a second-half substitute during Bayern's 2-1 home success over Bayer Leverkusen on Saturday, confirmed his delight at signing his new deal in a statement on the club's official website.
"I'm very happy to play for FC Bayern for another year," the winger said. "This great club and the city have become my home, both in terms of sport and in private."
The former Marseille ace is now fully focused on helping Bayern enjoy even more success, as he looks to add to the six Bundesliga titles and one Champions League crown that he has already won with the club.
He added: "I'm looking forward to many more beautiful moments together with the FC Bayern fans, and I want to play my part in the team's success in the next one and a half years."