Kronwall was drafted in the 9th round, 285th overall, by the Toronto Maple Leafs in the 2002 NHL Entry Draft. He is the younger brother of NHL defenceman Niklas Kronwall. Staffan represented his country at the 2002 World Junior Hockey Championships, recording 0 points and 4 penalty minutes in 7 games for Sweden. Kronwall was also named to the Swedish national team for exhibition matches against Switzerland leading up to the World Championships. Kronwall honed his skills as a defenceman in the Swedish Elite League before making his debut in the NHL.
In 2005-06, his first season in North America, Kronwall split his playing time between the Maple Leafs and their AHL affiliate, the Toronto Marlies. While playing for the Marlies, Kronwall enjoyed moderate offensive success, scoring 11 points in 11 games before being called up by the Maple Leafs. While in the NHL, Kronwall played a consistent defensive game, registering only one point in 34 games but maintaining a respectable -3 plus/minus rating with a mediocre Maple Leafs team. After suffering a knee injury, Kronwall was returned to the Marlies for the 2006-2007 season. However, in 2007-08, Kronwall was recalled to the Maple Leafs, where he played in 18 games. Kronwall did not record a point in these games. Kronwall has since returned to the Marlies, and is a current member of the 2008-09 AHL roster of the team.