Kubík moved to Major League Soccer in 1998, joining the expansion team Chicago Fire, and soon became recognized as one of the best defenders in the league. While helping the Fire to win both the MLS Cup and the U.S. Open Cup in their inaugural year, Kubík was named the MLS Defender of the Year for his role in marshalling the Chicago defence; he started 31 games for the Fire, and scored 7 goals and 8 assists, tremendous numbers for a defender. Kubík continued to be a valuable attacking force from the back in 1999, registering 5 goals and 8 assists, and was named in the MLS Best XI for a second time. He struggled with injuries in 2000, playing in only 13 games, but was effective when able to play, scoring 3 goals and 6 assists.
The Fire traded Kubík to the Dallas Burn during the 2001 offseason in exchange for Sergi Daniv. Kubík's final year was again beset by injuries, and he only managed to play 11 games for the Burn. Kubík retired due to injury at the end of the 2001 MLS season and returned to the Czech Republic.
He had a brief spell working for Hradec Králové and in the summer of 2006 was appointed as manager of Polish side Śląsk Wrocław. However he was sacked in October 2006 after just 11 league games in charge.
He was appointed manager of the EnglishFootball League Two side Torquay United on 27 November 2006 through his close friendship with Torquay chairman Chris Roberts. . Despite his impressive playing career, his lack of managerial experience and contacts in England was a problem, not aided by Roberts appointing Richard Hancox as Kubik's assistant. Torquay struggled under Kubik, winning just twice in 15 games, and he left club by mutual consent on 5 February 2007, with Torquay deep in relegation trouble. Roberts also resigned as chairman later that month. Torquay would be relegated at the end of the season, ending a 79 year spell in the Football League.