Radice played in Serie A for teams such as Milan, Triestina and Padova. Initially a member of the Milan Youth squad, he struggled to find space in the first team; he made his Serie A debut with Milan on 25 March 1956, in a 0–0 away draw against SPAL. He made only 19 appearances in total during his first three seasons at the club, as Milan won the 1956–57 and the 1958–59 Serie A titles. He subsequently moved to Triestina and Padova to gain more playing time, where he impressed fans before being recalled to Milan. During his second stint with the club, he played a pivotal role in helping Milan to win the 1961–62 Serie A title and the 1962–63 European Cup. However, serious injuries to his knee cut his playing career short, and he retired in 1965. In total, he made 95 appearances for Milan, 75 of which came in Serie A, scoring 1 goal throughout his Milan career, which came in Serie A.