Martin A. Fleckman (born April 23, 1944) is an American professional golfer who played on the PGA Tour in the 1960s and 1970s.

Fleckman was born in Port Arthur, Texas. He credits Byron Nelson, Carl Lohren and Jim Hardy with teaching him how to play golf. At the age of 20 in 1964, Fleckman won the individual title at the Texas State Amateur. In 1965, he won the NCAA Championship while a student at the University of Houston, where he was a three-time All American member of the golf team: third-team in 1964, first-team in 1965 and 1966. He was a member of the Walker Cup team in 1967.

While still an amateur, Fleckman played in the 1967 U.S. Open at Baltusrol Golf Club. He led the tournament after the first three rounds, but shot 80 in the final round amid a final-round surge by eventual champion Jack Nicklaus. The last amateur to lead the U.S. Open after three rounds was Johnny Goodman in 1933.

Fleckman won the 1967 Cajun Classic Open Invitational in his first start as a member of the PGA Tour. He is only one of four other players in Tour history to win his first tour event, and the first to do it. He has since been joined by Ben Crenshaw (1973), Robert Gamez (1990) and Garrett Willis (2001). His best finish in a major is T-4 at the 1968 PGA Championship.

Fleckman was inducted into the Texas Golf Hall of Fame in 1986 and the University of Houston Hall of Honor in 2006. He also received the prestigious 2007 Teacher of the Year Award for the Southern Texas Section of the PGA. He currently works as director of golf instruction at Blackhorse Teaching Center in Texas.