Despite his Argentine origins, Montuori began his career with Universidad Católica in Santiago, Chile, in 1953, winning the Chilean Primera División in 1954, scoring 24 goals in 26 league appearances for the club. He subsequently moved to play with ACF Fiorentina in Italy in the summer of 1955, at the request of club president Enrico Befani, and was handed the number 10 shirt. He played at the club from 1955 to 1961, making 162 Serie A appearances, and scoring 72 goals. In the Coppa Italia he played 13 matches scoring 6 goals, and in the 1956–57 European Cup he played 7 games and scored 1 goal, helping the team to the final. He also played 2 matches in the Mitropa Cup with Fiorentina.