Hellberg was selected 38th overall by the Nashville Predators in the 2011 NHL Entry Draft, and was the first goaltender selected in the draft. Hellberg almost didn't make the trip from Sweden to St. Paul, Minnesota, for the draft, citing it was "50-50" that he'd even be drafted. Because of the last minute decision to come, the only person with him was his agent. Technically, he was the first player to wear the new, redesigned Nashville jersey. The home gold version had still not been unveiled by the team and the road white debuted at the 2011 NHL Entry Draft. Additionally, the Predators did not have a first round pick, giving Hellberg the honor of becoming the first player to wear it. During the 2012–13 season, Hellberg appeared in 39 regular season games with the Milwaukee Admirals of the American Hockey League and two games with the Cincinnati Cyclones of the ECHL. He added four more games with Milwaukee during AHL post-season. On 26 October 2013, Hellberg made his NHL debut with the Nashville Predators, playing 12 minutes after replacing starter Carter Hutton in a game against the St. Louis Blues. With the Predators system crowded at both NHL and AHL levels, he was assigned to ECHL affiliate, the Cyclones, to finish the 2013–14 season. On 1 July 2015, Hellberg was traded to the New York Rangers for a 6th-round pick in the 2017 NHL Entry Draft. Hellberg was assigned to the Hartford Wolf Pack upon his arrival in New York, but was called up on 18 December to serve as a backup to Henrik Lundqvist while Antti Raanta was recovering from a head injury. Hellberg took the ice in a 20 December game against the Washington Capitals after Lundqvist allowed five goals, including four in the second period; Hellberg allowed two goals in the third period as the Rangers eventually lost the game 7–3. On 30 December, after Raanta was cleared to return, Hellberg was sent back down to the Wolf Pack. Hellberg was called up to the NHL three times during the 2016–17 season, the first call-up came on 15 January 2017 after Raanta suffered a lower body injury against the Montreal Canadiens. As a result, Hellberg was called up to the NHL to back up Lundqvist for one week while Raanta recovered. Hellberg took the ice once as he replaced Lundqvist during the third period of the Rangers 17 January game against the Dallas Stars; the Rangers lost the game 7–6 despite rallying from a 7–3 deficit. He was called up again in March after Lundqvist suffered a hip injury. He served as Raanta's backup for 5 games, but did not see any ice time. Hellberg was called up a third time for a season-ending back-to-back set of games, after Raanta suffered another lower body injury. Hellberg sat on the bench as Lundqvist's backup in the first game, but Hellberg made his first NHL start in the second game against the Pittsburgh Penguins. He stopped 22 of 24 shots as the Rangers won the game 3–2. As an impending free agent, Hellberg left the NHL and signed a one-year contract to be the starting goaltender of Chinese club, Kunlun Red Star of the KHL, on 25 May 2017. In the 2017–18 season, despite registering just 16 wins in 51 games, Hellberg was a standout for the underperforming Kunlun, posting a.926 save percentage. Having earlier signed a one-year extension with Kunlun during the season, Hellberg was traded the following off-season by the Red Star, to perennial contending club, SKA Saint Petersburg in exchange for financial compensation on May 28, 2018.
