Maschio started playing at Arsenal of Lavallol to later move to Quilmes Atlético Club where he proved himself a prolific goal-scorer. He joined Racing Club in 1954, and transferred to Italy in 1957. He had been linked with a move to Juventus in 1956, but their interest cooled following the international between Italy and Argentina in Buenos Aires that year when he looked ineffective. Instead he signed for Bologna in 1957, but although he paired up with Bernard Vukas there, he was unable to recreate the form he showed at Racing.
From Bologna Maschio moved to Atalanta who bought a half-share in him during the 1959-60 season. In Bergamo Maschio regained the form that had taken him to international prominence scoring heavily, and creating numerous chances for his colleagues. At Atalanta Maschio moved from playing as central striker to a deeper role which allowed him to use his vision and creativity. So impressive was his form at Atalanta that he moved to Inter in 1962. However, Maschio failed to fit in with manager Helenio Herrera who used him as a central striker and his time in Milan was of limited success. Following his time at Inter, Maschio briefly played with Fiorentina.
His performance brought him to the Italian national team to play in the 1962 FIFA World Cup. He returned to Racing in 1966 to win the Copa Libertadores and Intercontinental Cup in 1967, and to end his career with the club of Avellaneda with 44 goals in 139 matches.
Maschio played 12 games for the Argentina national football team between 1956 and 1957, scoring 12 goals, he helped Argentina to win the Copa America 1957, he was the top scorer in the tournament with 6 goals.
Maschio also played two games for the Italian team in 1962, scoring no goals. In the 1962 World Cup played in Chile, Maschio was the captain of the Italian team and one of the protagonists of the Battle of Santiago incidents in the match against the Chilean team, in which Chilean player Leonel Sanchez broke his nose.
Antonio Angelillo, Omar Sivori and Humberto Maschio acquired the nickname "the Angels with Dirty Faces" when they moved en masse to Italy in the latter part of the 1950s. The name was given to them on account of their typically South American colour and flair. They were also known as "The Trio of Death" because of their clinical ability in scoring goals.
Maschio coached the Argentine national team in the first half of 1969 and the Costa Rica national team 1972.