The Maple Leafs' final regular-season game is at the Winnipeg Jets on May 14, three weeks away.
"He's played very well for us this season," Toronto coach Sheldon Keefe said Friday. "He's really come in and I think delivered on what we wanted him to provide in terms of stability on our third pairing, penalty-kill minutes, a little bit of a different look and feel to our defense."
Bogosian was injured when he lost an edge pursuing the puck and hit the boards in the second period of a 6-3 loss at the Vancouver Canucks on Tuesday.
He signed a one-year, $1 million contract with the Maple Leafs on Oct. 10 after helping the Tampa Bay Lightning win the Stanley Cup last season.
"He's experienced … and being a part of that run in Tampa," Keefe said. "So certainly, you're going to feel that absence. I know he's going to do everything that he can to get back, and our medical staff is going to try and get him up and running as soon as possible."
Bogosian, who had four assists in 45 games, was relied on for his defensive and physical play. He led the Maple Leafs with 49 penalty minutes and had 67 hits and 31 blocked shots.
Rasmus Sandin likely will get the first opportunity to replace Bogosian on the third defense pair with Travis Dermott. Sandin, who fractured his foot during a game with Toronto of the American Hockey League on Feb. 15, has played the past two games for the Maple Leafs. He has one assist in three NHL games this season.
"I feel stronger overall," Sandin said of his rehab. "I feel like I have more pop in my legs."
Defenseman Ben Hutton also is an option, Keefe said.
Hutton, who was acquired April 12 in a trade with the Anaheim Ducks for a fifth-round pick in the 2022 NHL Draft, has scored five points (one goal, four assists) in 34 games this season.
Toronto (29-13-5) leads the Winnipeg Jets by six points for first place in the seven-team Scotia North Division. The top four teams qualify for the playoffs.
The Maple Leafs visit the Jets on Saturday (7 p.m. ET; NHLN, CBC, SNO, SNP, NHL.TV).
