Musso was born in Rome and began his racing career driving sports cars before making his début on the Formula One circuit on 17 January 1954, driving a Maserati. In 1954 he won the Coppa Acerbo, a non-championship Formula One race. At Zandvoort, in the 1955 Dutch Grand Prix, Musso placed third in a Maserati. At the end of the 1955 Formula 1 season he switched to Ferrari. He shared victory in the 1956 Argentine Grand Prix with Juan Manuel Fangio, however his season was cut short after a crash in a sports car race at Nürburgring.