Vůjtek played two seasons for HC Vítkovice in the Czechoslovak Extraliga before coming to North America to play for the Western Hockey League's Tri-City Americans. He made his NHL debut with Montreal in the 1991–92 season, appearing in two games before returning the Americans. Vůjtek joined the Edmonton Oilers' organization before the 1992–93 season, and played 70 games with the Oilers over two seasons. During the 1994-95 NHL lockout, Vůjtek returned to Europe. He remained in the Extraliga and the SM-liiga of Finland until 1997, where he played for HC Vitkovice for two seasons and spent one season skating with Ässät.