Turning professional in 2011–12, Pánik was a member of the Norfolk Admirals team that set the longest win streak in professional hockey in North America, winning a record-breaking 28 consecutive victories that season. Pánik also helped the Admirals capture the Calder Cup championship in a 4–0 sweep over the Toronto Marlies. Due to the 2012–13 NHL lockout that cancelled nearly half of the regular season, Tampa Bay assigned Pánik, as well as 17 others, to the Syracuse Crunch, the Lightning's new AHL affiliate for the 2012–13 season. On 11 February 2013, several weeks after NHL play had resumed, the Lightning recalled Pánik, where he later scored his first career NHL goal on 23 February against Dan Ellis of the Carolina Hurricanes in a 5–2 victory. On 1 March, the Tampa Bay Lightning reassigned Pánik to Syracuse after playing nine games in the NHL, registering one goal from eight shots on net. At the end of the AHL regular season, Pánik had played in 43 games with the Crunch, recording 21 goals and 35 points, including an AHL-high 12-game point streak from 2 November through 1 December 2013, with 17. Pánik then helped Syracuse reach the Calder Cup Final, though the team fell to the Grand Rapids Griffins in a 4–2 series defeat. Pánik made the 2013–14 Lightning roster out of training camp to begin the regular season. Despite making the team, he saw his playing time dwindle as the season went on, however, and, after struggling to find consistency in his game, was demoted on 24 January 2014, to Syracuse. Several months later, on 5 March, Tampa Bay again recalled Pánik from the Crunch. He finished the regular season with 50 appearances for Tampa Bay, scoring three goals and ten assists for 13 points, in addition to Stanley Cup playoffgames played against the Montreal Canadiens in the Eastern Conference Quarter-finals. On 11 July 2014, Pánik signed a one-year, two-way contract extension with Tampa Bay. After failing to make the 2014–15 Lightning roster out of training camp, however, he was placed on waivers, where he was then claimed by the Toronto Maple Leafs on 9 October 2014. On 25 October, he scored his first goal as a Maple Leaf in a 4–1 loss to the visiting Boston Bruins. Pánik experienced a breakout season in Toronto, setting career-highs in games played, goals scored and points. Following this noteworthy campaign, on 1 July 2015, Pánik signed a one-year, $925,000 contract with the Maple Leafs. Pánik was expected to play with the Maple Leafs in the 2015–16 season; however, he was beaten on the depth chart by new additions such as Brad Boyes and P. A. Parenteau. Additionally, the Maple Leafs claimed defenceman Frank Corrado off waivers on 6 October 2015. Having reached the maximum roster size, Pánik was placed on waivers with the purpose of being sent down to the Toronto Marlies. Pánik cleared waivers the following day. On 3 January 2016, after playing 32 games with the Marlies, Pánik was traded to the Chicago Blackhawks in exchange for Jeremy Morin. He finished the season with the Blackhawks and was re-signed to a one year, $875,000 contract extension. Pánik scored his first career NHL hat-trick against the Nashville Predators on 15 October 2016. Pánik tallied a career-high 22 goals and 22 assists during the season. On 11 May 2017, he signed a two-year extension worth $2.8 million per year with the Blackhawks. On 10 January 2018, Pánik was traded to the Arizona Coyotes in exchange for Anthony Duclair and Adam Clendening. On 1 July 2019, as a free agent from the Coyotes, Pánik left to sign a four-year $11 million contract with the Washington Capitals.
In July 2016, Pánik married his long-time girlfriend, Nikola Kochanová. In April 2018, Pánik was arrested after refusing to leave the entrance of Bevvy, near Scottsdale, Arizona. He was later released with criminal citation.
