The Bruins plan to retain their rights to Forsbacka-Karlsson by making him a qualifying offer, Eric Russo of the team's official site reports.
Forsbacka-Karlsson intends to sign a contract with Vaxjo of the SHL for the 2019-20 season.
Forsbacka-Karlsson was sent down to AHL Providence on Monday.
Forsbacka-Karlsson registered an assist on the game-winning goal during Thursday's 5-2 win over the Blues.
Forsbacka-Karlsson tallied an assist and won three of five faceoffs during Thursday's 4-2 loss to the Capitals.
Forsbacka-Karlsson will be a healthy scratch Saturday, when the Bruins play host to the Predators, per Matt Kalman of NHL.com.
Forsbacka-Karlsson scored the game's opening goal on Saturday as the Bruins topped the Maple Leafs 6-3.
The Bruins reassigned Forsbacka-Karlsson to AHL Providence on Sunday, Mark Divver of The Providence Journal reports.
Forsbacka-Karlsson is currently back home in Sweden tending to personal matter, Mark Divver of The Providence Journal reports.
Forsbacka-Karlsson was shipped off to AHL Providence on Friday.