The cause of death wasn't immediately known, said Marc Lipkin, director of publicity for Chicago-based Alligator Records. Lipkin added that he believed Hunter lived in Phoenix for the past decade or more.
Hunter also was a singer-songwriter whose best-known tracks are "El Paso Rock" and "Alligators Around My Door."
Born John Thurman Hunter Jr. in Ringgold, Louisiana, Hunter grew up in Arkansas and Texas and bought his first guitar after seeing B.B. King in concert.
James Brown, Buddy Holly, Etta James and Albert Collins reportedly attended shows by Hunter, who also became a mentor to then-teenager Bobby Fuller of "I Fought the Law" fame.
It was at the Lobby Bar that Hunter developed his showmanship. He was known for holding his guitar by the neck in one hand while continuing to play. With his free hand, Hunter would reach up, grab a rafter above the stage and start to swing but never missed a beat.
The antics inspired the title of Hunter's 1997 album Swingin' From The Rafters, which made him an internationally touring festival headliner.
Hunter released independent CDs in 2003 and 2009 and reportedly continued to play regularly until he was 80.
He's survived by his wife, Gayle, and brother, Tom. Funeral services were pending.