The association was founded in Geneva in 1932, two years after the sport was officially recognized by the IOC. Before 1934, basketball was under the umbrella of the International Amateur Handball Federation. Its original name was Fédération Internationale de basket-ball amateur.

The rapid growth of basketball in the 1920s and 1930s, primarily at the American high school and college levels, led to a worldwide interest in basketball competition. This led to the creation of the Federation Internationale de Basketball Amateur (FIBA) in 1932.