The league said Saturday night on Twitter that it was made aware of the social media posts and plans to conduct a full investigation.
An Instagram account, appearing to belong to Kane's wife, Anna, posted in a story: "How does the NHL let a compulsive gambling addict still play when he's obviously throwing games to win money? Hmm maybe someone needs to address this."
She added: "Can someone ask [commissioner] Gary Bettman how they let a player gamble on his own games? Bet and win with bookies on his own games?"
In a separate story post, Anna Kane accused her husband of spending lavishly partying in Europe while asking her to sell her wedding ring to survive and wrote about not being able to afford baby formula for their child.
The NHL said: "The integrity of our game is paramount and the League takes these allegations very seriously."
A Sharks team spokesman wrote in an email to The Associated Press that: "The San Jose Sharks have been in contact today with the National Hockey League about the serious allegations made against Evander Kane. We support a full and transparent investigation into the situation to maintain the integrity of the game and consistency with our team values.''
Kane's gambling history and finances have been public knowledge for some time. A Las Vegas Strip casino sued Kane in 2019, alleging he failed to repay a $500,000 gambling debt racked up during a playoff series against the Golden Knights.
Since the Supreme Court paved the way for legalized sports gambling in the U.S. and more states have adopted it, the NHL has embraced the possibilities and made several partnerships with sportsbooks and other betting organizations.
Reached by email before the league's announcement, deputy commissioner Bill Daly said only a statement would be coming. The league said it would not make any further comments at this time.
A message sent by The Associated Press to Kane's agent was not immediately returned.
Kane, 29, is three seasons into a $49 million, seven-year contract. He's with his third organization after being drafted by and debuting with Atlanta/Winnipeg and a stint in Buffalo. According to Capfriendly, which charts hockey salaries, he has made just under $56 million during his NHL career.
Last season, he had 22 goals and 27 assists in 56 games.
The Associated Press contributed to this report.