The reason for the leave and how long the 34-year-old defenseman will be away from camp were not disclosed.
"Let's just put it this way, there's nothing sinister to this," coach Paul Maurice said. "You start going down the list and then the process of elimination ... he has his right to privacy in this. Like I said, there's nothing sinister to it. He needs some time and he was given that."
Byfuglien had 31 points (four goals, 27 assists) in 42 games last season and eight points (two goals, six assists) in six Stanley Cup Playoff games. He missed 15 games from Dec. 31-Feb. 5 because of a lower-body injury and missed 19 from Feb. 16-March 28 because of a different lower-body injury.
"Dustin is a big part of our family here," general manager Kevin Cheveldayoff said. "There's always an open policy for discussions. We always care about people of our family. One thing I will say, healthwise, everything is good for him and his family. But again, from our standpoint, we support Dustin and look forward to the resolution."
The Jets enter camp without three other key defensemen from last season. Jacob Trouba was traded to the New York Rangers on June 17, Tyler Myers signed as free agent with the Vancouver Canucks on July 1, and Ben Chiarot signed with the Montreal Canadiens on July 4. Winnipeg allowed 243 goals last season, 17th in the NHL, after allowing 216 goals (fifth) in 2017-18.
Byfgulien is entering his 10th season with the Winnipeg Jets/Atlanta Thrashers after playing his first five NHL seasons with the Chicago Blackhawks. He has 525 points (177 goals, 348 assists) in 869 NHL games.
Maurice said he didn't know how Byfuglien's absence will affect Winnipeg's defense pairings.
"Well, we don't know if it impacts it at all," Maurice said. "For tomorrow's skate it will. But we'll get into timelines again, and I don't have those answers for you. We've got some new faces back there, and camp is important for them, but if you're looking for silver linings, there's more games now, possibly, if Dustin misses games, to take a look at some of those guys."
Among those new defensemen are Neal Pionk, acquired from the Rangers in the Trouba trade; Anthony Bitetto, who signed as a free agent July 2; Luke Green, a third-round pick (No. 79) in the 2016 NHL Draft; and Ville Heinola, the No. 20 pick in the 2019 NHL Draft.
NHL.com staff writer Tim Campbell contributed to this report