That equals the record set by former NHL forward Doug Jarvis from 1975 to '87. Yandle, 35, can break the mark by taking a shift in the Flyers' game at the New York Islanders on Tuesday night.
Yandle took his first shift one minute and 15 seconds into the first period of the 3-1 loss. According to the NHL, that's all he needed to do to tie the record. Firmly on the back end of the Flyers' depth chart, the veteran had one shot on net Monday, skating 21 shifts that covered 13:39 of ice time in the loss.
"It wasn't really something I expected. I just kind of never really thought about it," he said after the game. "I saw the guys standing for me, cheering. All the fans. It definitely meant a lot."
Jarvis didn't miss a regular-season game from his NHL debut on Oct. 8, 1975, with the Montreal Canadiens through the end of the streak on Oct. 10, 1987, with the Hartford Whalers.
Yandle's streak didn't begin in his rookie season but rather in his third season in the NHL. Since March 26, 2009, he has appeared in every game, not missing one for injuries, illness, suspensions or scratches.
"It's an incredible accomplishment," Flyers interim coach Mike Yeo said. "No. 1, you have to love the game, you have to battle through sickness, injuries. A level of professionalism to come to the rink every day and be ready to go. And he's a phenomenal teammate and I thought he played a hell of a game tonight."
There were close calls. The streak was threatened when the Florida Panthers considered making him a healthy scratch at the start of last season. Yandle also had several teeth knocked out in a November 2019 game and required extensive dental work but returned that same night wearing a full-face cage and then played the following afternoon.
"It's how hockey players are built. You play through as much pain as you can. There have obviously been some times when I have not felt great, when it was tough sledding. But you try to battle through it and help out your team," Yandle said Sunday.
For his career, Yandle has now played in 1,074 games with the Phoenix/Arizona Coyotes, New York Rangers, Panthers and Flyers, who signed him as a free agent last offseason. So far this season, Yandle has 13 assists in 41 games, skating to a minus-22.
Heading into game No. 964, Yandle had taken 25,070 shifts, the fifth most in the NHL during that span. He has been on the ice for 20,863 minutes and 26 seconds, which is the sixth most in the NHL.
While Yandle is poised to set the NHL "iron man" record, there's another player with an active streak right behind him: Arizona Coyotes winger Phil Kessel, 34, has played 940 consecutive games, beginning Nov. 3, 2009.