The defenseman sustained the injury when he collided with Boston Bruins defenseman Derek Forbort in the second period of a 3-2 loss on Saturday.
"We missed him out there," Coyotes coach Andre Tourigny said postgame. "He's on fire. It's tough, especially with quality minutes [Chychrun] plays."
Chychrun has scored 21 points (seven goals, 14 assists) in 47 games this season and leads the Coyotes in average ice time (22:59). He entered the Bruins game with five points (four goals, one assist) in his previous two games and 10 points (five goals, five points) in his previous six.
Selected by the Coyotes in the first round (No. 16) of the 2016 NHL Draft, Chychrun's name has been brought up ahead of the 2022 NHL Trade Deadline on March 21. He led NHL defensemen with 18 goals last season and is in the third season of a six-year contract he signed on Nov. 13, 2018.
"Well, if you think about it, he's a No. 1 [defenseman] that's 23 years old with a team-friendly contract and someone that generated 18 goals the year before, so he has a lot of impact on your team," Arizona general manager Bill Armstrong said last week. "You'd be crazy to move him unless it moved your team forward."
The Coyotes (19-36-4) are in last place in the Central Division. They defeated the Ottawa Senators 5-3 on Monday.
Earlier in the day, Arizona recalled Cam Dineen from Tucson of the American Hockey League. The rookie defenseman has four assists in 14 NHL games this season.