Born in Muzzana del Turgnano, Frossi began his career as a professional footballer with Udinese, and, after a long stay in Serie B (with Padova, Bari, and L’Aquila), he was acquired by Ambrosiana Inter, where he made his debut on 21 June 1936, in Mitropa Cup. After that, Frossi was called up for the 1936 Summer Olympics by Vittorio Pozzo, the coach of the Italian national side, leading the team to the victory of the tournament with his prolific performances. In the following years, Frossi played with Inter from 1936 until 1942, winning the “Scudetto” or league championship, twice in 1938 and 1940, as well as the Coppa Italia in 1939. He scored 49 goals in 147 matches with Inter, 40 of which came in the league, in 125 appearances. During World War II, he later also played with Pro Patria between 1942 and 1943, and Como in 1945, before retiring.