Lach's number, 16, was retired by the Montreal Canadiens in 2009 in an emotional ceremony at the Bell Centre.
Friends and fans paid their respects on social media.
The Montreal Canadiens organization paid tribute by tweeting photos of Lach during his time on the Habs' Punch Line, in the 1940s.
NHL commissioner Gary Bettman released a statement on Saturday:
"The National Hockey League deeply mourns the passing of Elmer Lach — centre on Montreal's legendary 'Punch Line' with Toe Blake and Maurice Richard, owner of the sole assist on Richard's 50th goal in 50 games in 1944-45 and someone who, at 97 years of age, was just a few months younger than the League itself.
"The League sends heartfelt condolences to the family and friends of this three-time Stanley Cup champion, two-time scoring champion and 1945 Hart Trophy winner."
Prime Minister Stephen Harper extended his condolences on Twitter.
Fans reacted online to the news of the passing of the NHL's oldest living player.