Controversy erupted at the SportAccord convention in the Russian resort of Sochi after its chief Marius Vizer accused Bach of blocking his plans to set up multi-sports events.
The presidents of the International Association of Athletics Federations (IAAF) and International Shooting Sports Federation (ISSF) gave immediate notice at the Sport Accord convention that they are leaving the group in protest, officials said.
IAAF president Lamine Diack, FIFA's Sepp Blatter and FINA swimming federation boss Julio Maglioine were among 15 federation chiefs to sign a letter condemning Vizer's remarks to the convention where Bach was a special guest.
Vizer, head of the International Judo Federation, slammed Bach's much-vaunted reforms of the IOC and the creation of a new Olympic television channel.
"Mr President, stop blocking the Sport Accord strategy in its mission to identify and organise conventions and multi-sport games. Do not try to create a theory around which sports are and are not eligible for multi-sport games."
Vizer also said individual federations should have more power on the IOC. "The IOC system is expired, outdated, wrong, unfair and not at all transparent," said Vizer.
It has had an increasingly tense relationship with the IOC since candidates were stopped from making bid presentations at Sport Accord's annual convention, which is billed as the world's biggest sports business event.