Fabbri was born in Castel Bolognese. During his club career, he played for several teams. He made his career debut with Imola in 1938, and he moved to Forlì (1939–40) the next season, later playing for Atalanta (1940–42, 1947–50) for two seasons, and subsequently with Inter (1942–43, 1945–46), and Faenza (1944), returning to Inter for a season in 1945. He moved to play with Sampdoria during the 1946-47 season, before returning to Atalanta for three seasons. He also later played for Brescia (1950–51), and Parma (1951-55), also winning the 1953-54 Serie C title. He ended his career with Mantova F.C. (1955–57). He also made one appearance for the Italian youth side in 1942.
After retiring from football, Fabbri began a coaching career with Mantova in 1957, in Serie D, the team with which he had retired as a player. During his four years with the club, he took the club to Serie A during the 1961-62 season, winning the 1957-58 Serie D and the 1958-59Serie C titles. In 1962, he was awarded the "Seminatore d'Oro" award for best coach, and he was subsequently appointed the head coach of the Italian national side.
Fabbri was the head coach of the Italy national football team from 1962 to 1966, with a record of 18 wins, 6 draws and 5 losses, and led the team in the 1966 FIFA World Cup, where they were eliminated in the first round after surprisingly losing to North Korea; Fabbri was let go following Italy's elimination from the 1966 World Cup.