[5] Penguins assistant director of amateur scouting Randy Sexton praised Sundqvist following the draft by saying "He's big, he's rangy, he skates and plays very hard.

"[6] After his selection, Sundqvist was invited to the Penguins' Prospect Development Camp[7] before returning to his home country where he made his Swedish Elite League (SEL) debut with Skellefteå on 24 October 2012 against Frölunda HC.

[1] During the summer prior to the 2013–14 season, Sundqvist was invited to participate in the Penguins' Prospect Development Camp at the Consol Energy Center.

[27] Upon returning to the Wilkes-Barre/Scranton Penguins in the AHL, Sundqvist played on the team's third line alongside Dominik Uher and Tom Kostopoulos.

[1] In those 42 games, Sundqvist recorded a career high five points while playing on the fourth line and averaged nearly a minute on the penalty kill.

[47] While playing with the St. Louis Blues during the 2018 pre-season, Sundqvist suffered a head injury as a result of a hit from Washington Capitals player Tom Wilson, who was subsequently suspended.

[48] Sundqvist was immediately placed on the team's injured reserve to recover but returned to the lineup on 25 October after missing eight games.

[46] In spite of his hot start, by 2 January 2019, the Blues were in last place around the entire league, which resulted in a coaching and goaltender change.

[50] Along with the changes, Sundqvist recorded a career-high 31 points in 71 games to help the Blues qualify for the 2019 Stanley Cup playoffs.

Prior to the 2019 Stanley Cup Finals against the Boston Bruins, Sundqvist averaged 15:55 minutes of ice time and recorded nine points in 21 post season games.

At the time, Sundqvist received a two-minute minor penalty but was later suspended one game by the NHL's department of player safety.

[56] A few days later, after appearing in a total of 26 games and recording eight goals, Sundqvist was placed on the team's injured reserve to recover from a lower body injury.

[58] In late January, Sundqvist was again placed on the team's injured reserve to recover from a lower body injury suffered during a game against the Vancouver Canucks.

[60] Prior to the cancellation of the regular season due to the COVID-19 pandemic, Sundqvist was fined $5,000 for roughing Chicago Blackhawks defenceman Adam Boqvist during a game on 8 March.

[61] He also suffered a shoulder/AC joint injury during the Blues' final regular season game against the Anaheim Ducks, but used the NHL's pause in play as a time to recover.

On 21 March 2022, Sundqvist was traded to the Detroit Red Wings, along with Jake Walman, and a second-round pick in 2023 NHL Entry Draft, in exchange for Nick Leddy and Luke Witkowski[63] On 3 March 2023, the Red Wings traded Sundqvist to the Minnesota Wild in exchange for a fourth-round pick in the 2023 NHL Entry Draft.

[64] As a free agent from the Wild, Sundqvist was signed to a one-year, $775,000 contract to return to the St. Louis Blues for the 2023–24 season on 12 July 2023.

[66] During the season Sundqvist recorded six goals and 15 assists in 71 games before suffering a season-ending anterior cruciate ligament (ACL) injury on 25 March.