After two seasons with Ocelari Trinec of the Czech Extraliga, Panik was selected by the Tampa Bay Lightning in the second round (No. 52) in the 2009 NHL Draft. He was also chosen that year by defending Memorial Cup champion Windsor in the Canadian Hockey League Import Draft and joined the club for the start of the 2009-10 Ontario Hockey League season.

Although Windsor would go on to defend the championship, Panik would not be part of it. Shortly after returning from playing for Slovakia at the 2010 World Junior Championship, where he had five points in five games, Panik was traded by Windsor to Belleville on Jan. 6, 2010. He made his pro debut in 2009-10, playing five American Hockey League games with Norfolk.

In 2011-12, his first full pro season, Panik had 19 goals and 41 points in 64 games for Norfolk, which won an AHL-record 28 consecutive games. He had five goals and six points in 18 playoff games to help Norfolk win the Calder Cup that season.

He began 2012-13 with Syracuse of the AHL and was called up to the Lightning, making his NHL debut Feb. 11, 2013, against the Montreal Canadiens, and scoring his first NHL goal Feb. 23, 2013, against the Carolina Hurricanes. He had five goals and nine points in 25 games with the Lightning before being returned to Syracuse in time for a second straight run to the Calder Cup Finals.

Panik started 2013-14 with the Lightning but in January was assigned to Syracuse. Recalled March 5, 2014, Panik finished with three goals and 13 points in 50 games for the Lightning and made his Stanley Cup Playoff debut April 16, 2014, against Montreal. He also played for Slovakia at the 2014 Winter Olympics.

He was claimed on waivers by the Toronto Maple Leafs on Oct. 9, 2014, and spent the 2014-15 season with them, scoring 11 goals and 17 points in 76 games. On Jan. 3, 2016, Toronto traded Panik to the defending Stanley Cup champion Chicago Blackhawks for Jeremy Morin. Panik got his first NHL playoff point with an assist April 21, 2016, against the St. Louis Blues.