Stroppa started his playing career in AC Milan's youth system, and was loaned for two seasons at Monza, a "de facto" Milan feeder club at the time. He returned to Milan in 1989, making his professional senior debut for the club in the Coppa Italia on 23 August, in a 0–0 away draw against Parma; Milan later reached the Coppa Italia final, only to be defeated by Juventus. He made his Serie A debut on 27 August 1989, in a 3–0 away win over Cesena, marking the occasion by scoring a long-range goal. Stroppa finished his first season with the team by winning a European Cup, a European Super Cup, and an Intercontinental Cup in 1990, under coach Arrigo Sacchi.