The IBA, the long-standing ruling body of traditionally amateur competitions, such as the Olympics, is involved in a brawl with the International Olympic Committee (IOC) over financial, governance and ethical concerns.
The IOC took over running the boxing competition at this year's Paris Olympics.
IOC president Thomas Bach warned that boxing's national federations needed to find a new and "reliable" international partner for the IOC to be sure the sport features on the programme at the Los Angeles Games in 2028.
A decision is due early in 2025 on whether or not to keep the sport in the Games.
FFBoxe said it planned to join World Boxing.
World Boxing, which was founded in 2023 and boasts around 50 members, led by the United States, the United Kingdom, Germany, Australia and Brazil, is in discussions with the IOC to take over running the sport at the Games.
FFBoxe said the decision to "disaffiliate" from the IBA, was "motivated by the desire to guarantee French boxing its place at the Olympic Games and to reinforce the stability of its clubs".
It said it had been prompted to act by a letter from David Lappartient, President of the French Olympic Committee, and a candidate to replace the departing Bach as IOC president, pointing out that boxing was not, for now, on the 2028 Olympic programme.
The IBA is chaired by the Kremlin-linked Russian Umar Kremlev who sparked a damaging gender controversy during the Paris Olympics when he claimed that two women fighters had "genetic testing that shows that these are men".
The IOC, which leaves gender rules to the sporting bodies, cleared them to compete and expressed doubts about the IBA's testing and motivations.
The IBA responded with a chaotic press conference in Paris intended to clarify why it disqualified Algeria's Imane Khelif and Taiwan's Lin Yu-ting from its world championships in 2023 but then cited "medical confidentiality" as it failed to produce definitive evidence.
Both boxers won gold in Paris.
