According to a report in The Toronto Sun, Maple Leafs defenseman Wade Belak took offense to alleged comments from Avery and said the Rangers forward will suffer severe payback.
Before the Rangers' 3-2 shootout win over the Leafs on Saturday night, Avery shoved Leafs forward Jason Blake, then had words with Blake and Darcy Tucker. Avery and Tucker threatened each other with their sticks before the incident cooled.
"He's pissing guys off," Belak told The Sun. "He'll bring harm to himself and not too many guys around the league are going to be sad to see it. If he keeps this up, someone is going to kill him. One day he's going to say something the wrong way and he'll be clubbed.
"And I'm not saying it will be by me, either."
Avery later fought Tucker during the game, completing what is known as the Gordie Howe hat trick (goal-assist-fight) in the Rangers' win.
Colin Campbell, the NHL's director of operations, is investigating the incident, the Toronto Globe and Mail reported Tuesday.
Rangers GM Glen Sather did not allow Avery to talk with the media after the game.
"Everybody knows about Sean's antics, fighting and his ability to get under peoples' skin, but every once in a while he reminds people that he can play," Shanahan said, according to The Sun.
Avery has scored in each of New York's last two games.
Acquired last season by New York in a trade with Los Angeles, Avery injected a shot of energy and gave the Rangers a physical and emotional edge. But the 27-year-old forward's arbitration hearing with the team turned contentious when the Rangers, according to a New York Post story, referred to Avery as "a reasonably effective player as well as a detriment to team" in a brief given to the arbitrator.
The Post reported that management also said, "Avery is not a mature player. He plays, at times, like an individual rather than a member of a team."
"I have no idea what to say," Avery told the newspaper last August. "I don't know what this was about. I'm shocked."
In the past, Avery has drawn the ire of many around the league for saying "visor-wearing French-Canadians" were guilty of dirty play. When he was fined for diving, he blasted the league, saying that he was a target of other players.