The forward, who has seven goals and 12 assists in 17 games, was injured during the second period of the Flyers' 4-1 loss at the Boston Bruins on Thursday and has missed the past two games.
"It's a monstrous hole for us," coach John Tortorella said prior to a 5-4 shootout loss to the Montreal Canadiens on Saturday. "But it is what it is. We're going to have other guys take his ice time."
Forward Kevin Hayes also has 19 points (five goals, 14 assists).
Philadelphia also placed forward Scott Laughton on injured reserve Tuesday because of an upper-body injury. He is expected to be out approximately two weeks.
Laughton left the loss to the Canadiens at 1:47 of the third period after being checked into the boards by Montreal defenseman Kaiden Guhle, and he didn't play in a 5-2 loss to the Calgary Flames on Monday.
He has seven points (three goals, four assists) in 18 games this season. Laughton also has been the Flyers' only alternate captain this season; Philadelphia does not have a captain.
With Konecny and Laughton out, Philadelphia is missing five forwards projected in the preseason to play in its top nine. Forward James van Riemsdyk had surgery on his left index finger Oct. 30 and is expected to be out six weeks. First-line center Sean Couturier has not played this season and is recovering from back surgery on Oct. 27 that was expected to sideline him 3-4 months. Forward Cam Atkinson has not played this season because of an upper-body injury.
"It's next man up right now," defenseman Travis Sanheim said Monday. "Obviously key guys out with injuries and we've just got to find a way to stick together as a group and continue to fight through this and find a way to win some hockey games."
Forward Wade Allison, who has missed five games with an oblique muscle strain and a hip pointer sustained Nov. 12, is expected to be out 2-3 weeks. The forward has four points (three goals, one assist) in 14 games.
The Flyers (7-8-4) have lost seven straight games (0-5-2). They next play at the Washington Capitals on Wednesday (7:30 p.m. ET; TNT, SN NOW).
"We want to win but it's not like it's a lack of effort right now," goalie Carter Hart said. "Obviously it's tough, we're losing a lot of guys, but can't control that, it is what it is. … Obviously it's a challenge but it's just something that we have to manage and deal with and find ways around it and find ways for guys to step up, including myself. And just find a way to get back in the win column."
The Flyers recalled forward Jackson Cates from Lehigh Valley of the American Hockey League on Tuesday. Cates didn't have a point in three games earlier this season with the Flyers; he has seven points (four goals, three assists) in 11 AHL games.
