The club announced last Friday that the veteran defenseman had been granted a leave of absence. While the reason and timetable weren't disclosed, head coach Paul Maurice said at the time that the blue-liner was "going to be fine," and it was "nothing sinister."
Byfuglien, 34, is entering the fourth year of the five-year, $38-million pact he inked with the Jets in February 2016.
Injuries limited him to 42 games in 2018-19, but he still collected 31 points and led the club in average ice time in his abbreviated campaign.
He's spent the last nine seasons with the organization after playing his first five campaigns with the Chicago Blackhawks, with whom he won a Stanley Cup in 2010.
The imposing rearguard ranks fifth on the Jets/Atlanta Thrashers franchise's games played list, sits third in assists, and slots in fourth in points.