Later in 1996, Kubina moved to Canada to join the Moose Jaw Warriors of the Western Hockey League (WHL), with which he scored 44 points in 61 games during the 1996–97 season.

He made his NHL debut in the 1997–98 season, although he spent most of the year playing for the Adirondack Red Wings of the American Hockey League (AHL).

Kubina spent most of the next season in the NHL, scoring 21 points, while playing occasionally in the International Hockey League (IHL) for the Cleveland Lumberjacks.

In the 2003–04 season, he was named to the NHL All-Star Game and won the Stanley Cup with Tampa Bay over the Calgary Flames in the Finals.

[1] On July 1, 2009, Kubina was traded to the Atlanta Thrashers (along with Tim Stapleton) in exchange for Garnet Exelby and Colin Stuart.