Born in Trieste, Cudicini began his professional career with Udinese in 1955, making his debut during the 1955–56 Serie B season, and obtained promotion to Serie A with the club. In his first season in the Italian top division, he collected 13 appearances throughout the season, and marked his Serie A debut with a clean sheet in a 2–0 home win over Palermo on 2 December 1956. In 1958, he joined Roma. After two seasons as the team's back-up goalkeeper behind Luciano Panetti, he was promoted to the team's starting goalkeeper in 1960, and retained the position for the next six seasons, collecting 166 league appearances, and winning the Inter-Cities Fairs Cup in 1960–61 and a Coppa Italia in 1964. He spent the 1966–67 Serie A season with Brescia, helping the club avoid relegation. In 1967, at the age of 32, he joined Milan, where he remained until his retirement in 1972, making 127 league appearances for the club and 183 appearances in all competitions under manager Nereo Rocco; he achieved notable domestic and international success with the club, winning the Serie A title and the Cup Winners' Cup in his first season, followed by the European Cup and the Intercontinental Cup in 1969, and finally the Coppa Italia in 1972. He is Milan's seventh-most capped keeper of all time, behind only Christian Abbiati (380), Sebastiano Rossi (330), Dida (302), Lorenzo Buffon (300), Enrico Albertosi (233), and Dario Compiani (221).