In the 2010–11 season, playing for Modo under-16 team, Hägg had a breakout year, leading the under-16 league in assists and points by a defenceman.

[6] Hägg made his NHL debut on 9 April 2017 against the Carolina Hurricanes in the last game of the Flyers regular season.

[8] Hägg led the NHL in hits with 232 and rookies in blocked shots before being pulled out of the lineup with a lower body injury on 10 March 2018.

[12] On 18 March 2021, Hägg suffered a shoulder injury in a 9–0 loss to the New York Rangers that kept him out of the lineup for two weeks.

He was leading the team in hits and short-handed time on ice while collecting eight points through 48 regular season games.

[18] He made his Red Wings debut in 3–0 shutout win over the Montreal Canadiens on opening night, taking a minor penalty for slashing.

[19] Hägg was placed on injured reserve with an undisclosed injury on 13 December, after registering two points in 13 games with Detroit,[20] and returned to action on 16 January 2023.

[23] As an unrestricted free agent from the Red Wings, Hägg joined his fifth NHL team in signing a one-year, $775,000 contract with the Anaheim Ducks for the 2023–24 season on 4 July 2023.

[30] After being recalled to the Golden Knights in mid-November,[31] Hägg subsequently debuted for Vegas on 21 November, playing just under nine minutes in a 3–2 victory over the Ottawa Senators.