Horák began his professional career with his hometown team HC České Budějovice of the Czech Extraliga, appearing in one game with the club in 2007–08 and eight more in 2008–09. He was selected by the New York Rangers in the fifth round, 127th overall, at the 2009 NHL Entry Draft. Additionally, Horák was selected by the Western Hockey League's (WHL) Chilliwack Bruins with the eighth overall pick in the Canadian Hockey League (CHL) import draft. Though he had little knowledge of English, Horák moved to Canada to join the Bruins for the 2009–10 WHL season.