Boqvist made his Swedish Hockey League debut playing with Brynäs IF during the 2015–16 SHL season.

[3] Boqvist's goal, which tied the game 1–1 in the first period, caused controversy by the play of Wayne Simmonds.

[3][4] On 22 July 2022, Boqvist agreed to his qualifying offer with the Devils, re-signing to a one-year, two-way contract for the 2022–23 season.

[12] This time, however, he would stick with the big club, finding a comfortable role on Boston's fourth line with his speed.

Boqvist scored his first NHL playoff point in game 1 of the first round series against the Toronto Maple Leafs, an assist on a goal by John Beecher.