Minto made his debut for Chelsea in a 6–2 Cup Winners' Cup win against Czech side FK Viktoria Žižkov, and played in every round of the side's run to the semi-finals. His time at Chelsea was plagued by injuries, but he was nevertheless a regular member of the Chelsea defence when fit. In 1996–97, he was an important part of the side's run to the 1997 FA Cup Final, which they won, defeating Middlesbrough 2–0 in what proved to be his last game for the club. He scored five goals in 72 appearances for Chelsea, all of which came in his final season.