Rask was selected in the second round of the 2011 NHL Entry Draft by the Carolina Hurricanes. On 29 June 2011, he was selected third overall by the Calgary Hitmen of the WHL in the 2011 CHL Import Draft. While playing in his first year of major junior hockey with the Hitmen, Rask was signed to a three-year entry-level contract with the Carolina Hurricanes on 20 October 2011. At the time of his signing, Rask led the Hitmen in points with 10. At the conclusion of his rookie season with the Hitmen, Rask was named the team's Rookie of the Year. Rask began the 2012–13 season with the Hurricanes American Hockey League affiliate, the Charlotte Checkers but was reassigned to the WHL after playing in 10 games. During that season, Rask was selected to play for Team Sweden at the 2013 World Junior Ice Hockey Championships. Although Team Sweden qualified for the gold medal round, they lost to the United States 3–1. The following season, Rask spent the entire 2013–14 season with the Charlotte Checkers in the American Hockey League. Although Rask began the season with 10 points in 10 games, he experienced a 24-game goal drought that was snapped in a 5–2 win over the Oklahoma City Barons on 10 January. Rask ended the season with 39 points in 76 games. Rask cracked the Hurricanes roster for the 2014–15 season, and made his NHL debut on 10 October against the New York Islanders. He scored his first career NHL goal on 3 November against the Los Angeles Kings. After recording a career-high 48 points in the 2015–16 NHL season, Rask signed a six-year, $24 million contract with an AAV of $4 million per season with the Hurricanes on 12 July 2016. Rask was named an alternate captain for the Hurricanes during the 2016–17 season. He shared the alternate captain title with Jordan Staal, Justin Faulk, and Jeff Skinner. Rask was later protected by the Hurricanes in the 2017 NHL Expansion Draft. During the offseason prior to the 2018–19 season, Rask underwent surgery to repair two fingers he injured while preparing food. He made his season debut for the Hurricanes on 21 November 2018 against the Toronto Maple Leafs.
Minnesota Wild
On January 17, 2019, Rask was traded by the Hurricanes to the Minnesota Wild in exchange for winger Nino Niederreiter.
