Futsal is a sport created in Uruguay in 1930. In 1965, the South American Indoor Soccer Confederation (CSFS) was created, the first international organization of the sport, currently affiliated with the AMF and in 1971 founder of the International Futsal Federation. (FIFUSA), direct predecessor of the AMF. In 1982, FIFUSA directly organized the first of three world championships that it would hold until its dissolution in 1990, although later the Pan American Futsal Confederation (PANAFUTSAL), an entity created after the disappearance of FIFUSA, organized four more world cups in the name of of the old federation until the foundation of the AMF in 2002.

FIFUSA and FIFA had a dispute over the use of the name "soccer", which was resolved in the 1980s, reserving "futsal" only for activities carried out under FIFA supervision. As a result of this, FIFUSA decided in 1985 to name the sport as "futsal"; name that was later also appropriated by FIFA itself.

In 1990 the South American federations and the rest of the continent formed the Pan American Futsal Confederation (PANAFUTSAL). This organization, created after the disappearance of FIFUSA due to economic problems, signed a letter of intent with FIFA in 2000 to join it. However, the agreement did not prosper and the members of PANAFUTSAL created a new sports association to which national federations from other continents joined. Thus, in December 2002 the World Futsal Association (AMF) was founded, made up of the former member federations of FIFUSA (previous organization).

Since its foundation, it has organized 4 World Cups: Paraguay 2003, Argentina 2007, Colombia 2011 and Belarus 2015, as well as the women's futsal World Cups: Reus 2008 (Spain) and Barrancabermeja 2013 (Colombia). In turn, it has organized the 2007 World Cup in Russia, the first children's futsal world cup in Quito 2003, the U-20 World Cup in Concepción 2014 and the U-17 World Cup in Paraguay 2016. By management of the Colombian Football Federation of Salón, an entity affiliated to the AMF, managed to include futsal in the 2013 Cali World Games as an exhibition sport, incidentally registering the AMF with the organizing entity of the games as official futsal councilor: the International Association of World Games (the IWGA in English), an entity that in turn is supported by the International Olympic Committee (IOC), organizer of the Olympic Games.