Barretto died at Hackensack University Medical Center in Hackensack, New Jersey, George Rivera said in a statement. Barretto had undergone heart bypass surgery in January, according to press reports.
Music critics said Barretto was key to the introduction of the driving salsa beat of the conga drum to jazz music.
"The first thing that came to my mind was passion," said Nat Hentoff, a noted jazz critic and columnist at The Village Voice in New York. "I first heard him with (fellow percussionist and bandleader) Tito Puente, who had this enormous spirit and sense of polyrhythm, and Ray was able to keep right up with him."
Jason Koransky, editor of the jazz magazine DownBeat, said, "The two musics, Latin and jazz, had a long history of intersecting, and they intertwined because of artists such as Ray."
"El Watusi" was released in 1962 and made it to the top 20 of the U.S. pop charts the following year. Barretto won a Grammy Award in 1989 for his performance of "Ritmo en el Corazon" with Celia Cruz.
The son of immigrants from Puerto Rico, New York-born Barretto played alongside jazz greats including Puente, Art Blakey and Lou Donaldson.