Kuka started and finished his career at Slavia Praha, playing with the club from 1989–93 and then from 2000–05. He has also played for 1. FC Kaiserslautern (1994–98), 1. FC Nuremberg (1998–99), and VfB Stuttgart (1999–2000). For the Czech national team, Kuka played 63 times, scoring 22 goals and was part of the runner-up squad at Euro 96 and also took part at Euro 2000. Kuka also played 24 times, scoring seven goals, for Czechoslovakia. Retired in May 2005, he has shortly worked as a manager in FK Marila Příbram (another Gambrinus league team) and then became football agent.