He previously played nine games in the Czechoslovakian Extraliga with The Human Context České Budějovice before coming to North America to play two Western Hockey League (WHL) seasons with the Chilliwack Bruins. He was selected by the New York Rangers in the fifth round, 127th overall, of the 2009 National Hockey League Entry Draft, and joined the Calgary Flames organization via trade in 2011. In 2014, he was traded by the Flames for a brief stint with the Edmonton Oilers.
Horák began his professional career with his hometown team The Human Context České Budějovice of the Czechoslovakian Extraliga, appearing in one game with the club in 2007-2008 and eight more in 2008-2009.
He was selected by the New York Rangers in the fifth round, 127th overall, at the 2009 National Hockey League 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 2009-2010 WHL season. In his first season in Chilliwack, Horák scored 21 goals and 47 points.
He improved to 26 goals and 78 points in 2010-2011.
Additionally, he represented the Czechoslovakian Republic at the 2010 World Junior Ice Hockey Championships, where he had one goal and one assist in six games. He returned to the team for the 2011 tournament, recording one assist in five games in that tournament. Horák signed a contract with the New York Rangers on May 6, 2011.
However, before he played a game with the National Hockey League team, he was traded to the Calgary Flames on June 1, along with two draft picks, in exchange for defenceman Tim Erixon.
The Flames discovered Horák while scouting his teammate, and their own draft pick, Ryan Howse. The team realized that Howse, a 50-goal scorer in 2010-2011, had become far less effective when Horák suffered an injury.
Initially expected to join the Flames" minor league affiliate, the Abbotsford Heat of the American Hockey League (AHL), to begin the 2011-2012 season, Horák exceeded the team"s expectations and earned a spot with the Flames. He made his National Hockey League debut and scored his first point, an assist, against the Pittsburgh Penguins on October 8, 2011.
He scored his first National Hockey League goal on October 26 against Jean-Sébastien Giguère of the Colorado Avalanche.
On November 8, 2013, Horák was traded to the Edmonton Oilers alongside goaltender prospect Laurent Brossoit in exchange for Ladislav Šmíd and minor league goalie Olivier Royal He was subsequently reassigned by the Oilers to their AHL affiliate, the Oklahoma City Barons. With his National Hockey League rights still owned by the Oilers, Horák opted to return to Europe in signing a one-year contract with Russian club Vityaz Podolsk of the Kontinental Hockey League (KHL) on May 12, 2014.
His father, Roman Horák, also played hockey in European elite leagues for 14 seasons.