Joe Puma (August 13, 1927 – May 31, 2000) was an American jazz guitarist.
Puma was born in the Bronx, New York. His first professional experience came with Joe Roland in 1949–50. He played in the band led by Cy Coleman. He acted as a session musician for many jazz musicians of the 1950s, including Louie Bellson, Artie Shaw's Gramercy Five, Eddie Bert, Herbie Mann, Mat Mathews, Chris Connor, and Paul Quinichette, Lee Konitz, and Dick Hyman; he also recorded extensively as a leader at this time. In the 1960s he worked with Morgana King, Bobby Hackett, Gary Burton, and Carmen McRae, and between 1972 and 1977 he and Chuck Wayne led an ensemble. He continued to perform and teach into the late 1990s.