Monzón had his first amateur fight on 2 October 1959. This first fight ended in a draw. Three years later, after a 73-6-8 amateur record, he became a professional. His first professional bout was held on 6 February 1963. He knocked out his opponent in the second round. In 1966, he won the Argentine middleweight title. In 1967, he won the South American middleweight title. After this success, Argentine boxing promoter Juan Carlos Lectoure pushed him into the international boxing scene by organizing fights with foreign boxers such as Douglas Huntley, Charles Austin, Johnny Brooks, Harold Richardson, Tommy Bethea, Bennie Briscoe (a ten-round tie) Manoel Severino and Eddy Pace.
