Spokesman John Dellapina said the league would have no comment until the investigation is completed.
Shaw was sent off for interference at 17:56 of the third period, hurting Chicago's chance for a comeback in what ended up being a 4-3 loss. While sitting in the box, Shaw pounded on the glass with his stick and then yelled what looked like a slur toward someone on the ice. No known audio exists of what he said in the noisy arena, but video of the incident quickly surfaced on social media and the You Can Play project swiftly tweeted that it was aware of the incident and planned to contact the NHL.
Asked twice about what happened, Shaw said he didn't remember.
"Being like I just said -- I'll repeat myself for you -- emotions are high," he said. "I don't know what was said. Obviously, I was upset with the call. I wasn't happy with the call."
Shaw scored a goal in the second period and had two assists in the loss, which left the defending Stanley Cup champion Blackhawks on the brink of elimination.
The team recently highlighted its partnership with the You Can Play project, which lobbies for equal and respectful treatment of all athletes without regard to sexual orientation. Defenseman Niklas Hjalmarsson and goaltender Scott Darling participated in a video supporting the group's mission.
"Our team pledges to support all our coaches, teammates and fans," Darling says in the video. "We believe that athletes should be judged by their character, work ethic and talent, not their sexual orientation or gender identity."
A national television audience heard Kobe Bryant shout the same slur in 2011 at a referee he thought had made a bad call during a basketball game. Chicago Bulls center Joakim Noah yelled it at a Miami Heat basketball fan who had been getting on him during a game a month later. Both quickly apologized, and the National Basketball Association hit them with large fines: Bryant was fined $100,000 and Noah $50,000.
Sacramento's Rajon Rondo was suspended one game in December for using the slur as he berated official Bill Kennedy, who subsequently came out as gay.
Major League Baseball in 2014 suspended Yunel Escobar, then a shortstop with the Toronto Blue Jays, for stenciling the word, in Spanish, onto his eye black.
Like MLB, The NHL has never had an openly gay player. The founder of You Can Play, Patrick Burke, works in the NHL's player safety office. He has championed the LBGT cause said earlier this year that he has met gay NHL players through the years.
Andrew Shaw faces disciplinary action for alleged gay slur
Scott Burnside analyzes the turn of events for the Blackhawks and Andrew Shaw's actions, which are under investigation by the NHL.
Le Batard on Shaw: How do you eradicate this?
Dan Le Batard wonders how the NHL and the sports world will be able to get its players to stop using homophobic slurs after seeing what Andrew Shaw appeared to say during Tuesday night's Blackhawks game.