Ribery suffered the injury in the 1-0 home loss to Lecce on November 30.
The news come as huge blow to a Fiorentina side that are struggling in Serie A this season.
"Franck Ribery today underwent surgery for stabilisation of the tibiofibular syndesmosis," a club statement read.
"The operation, carried out by Professor Gabel, was a complete success.
"The player will return to Florence on Sunday and begin his rehabilitation plan. He will resume exercise in two weeks.
"[He] is expected to resume full training in around 10 weeks' time."
The Viola have lost their last four league games and lie in 13th position, just three points above the relegation zone.
Any hopes of climbing up the table will be made harder on Sunday when Fiorentina welcome leaders Inter Milan to the Artemio Franchi Stadium.
Ribery joined Fiorentina on a free transfer in the summer after a 12-year career at German giants Bayern Munich, where he won nine Bundesliga titles and the UEFA Champions League.
The 36-year-old has played 11 Serie A games for Fiorentina so far this season, scoring two goals and providing two assists.
Ribery was named as the most valuable player in the Italian Serie A for the month of September.
In October, Ribery was banned for three league games and fined €20,000 for a post-match shove on an assistant referee following a home loss to Lazio.
