"UEFA's Control and Disciplinary Committee's verdict arrived on Thursday morning," the club said on their website. "David Bystron has been banned from all competitions, starting on January 3."
Viktoria general manager Adolf Sadek said Bystron would not appeal.
Viktoria, who made their maiden appearance in the Champions League after winning the Czech league title for the first time, did not name the substance but Czech media reported the banned substance as methamphetamine.
Viktoria defeated BATE 1-0 in Minsk on November 23 - a win that helped the Czech side gain a spot in the Europa League after finishing third behind Barcelona and AC Milan in their group.
Pavel Vrba's men will meet German club Schalke 04 in the Europa League's round of 32 matches on February 16 and 23.
Bystron, who scored a rare goal against AC Milan in Viktoria's last game in the group to start a late rally that led to a 2-2 draw, won the Czech title with Banik Ostrava in 2004 and the Bulgarian title with Levski Sofia in 2009.
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