A courtside microphone during ESPN's telecast on Wednesday night picked up Kyrgios saying that Australian player Thanasi Kokkinakis had slept with a player who is reportedly Wawrinka's girlfriend.
The $10,000 fine is the maximum allowed by the ATP rulebook for incidents of verbal abuse or unsportsmanlike conduct, but the ATP issued an additional fine of $2,500 to Kyrgios for unsportsmanlike conduct based on a comment he made to a ball person during the match.
The tour said Kyrgios has been served with a "Notice of Investigation," which begins a process to determine if his actions also constitute a violation of the "Player Major Offense" provisions set forth under "Aggravated Behavior" or "Conduct Contrary to the Integrity of the Game."
Kyrgios' troubles continued on the court Thursday, when he was beaten 7-5, 6-3 by John Isner and got into a verbal altercation with a fan.
Wawrinka tweeted Thursday morning that the Australian's words to him were "beyond belief" and urged tennis' governing body to take action.
"So disappointing to see a fellow athlete and colleague be so disrespectful in a way I could never even imagine," Wawrinka also tweeted.
"There is no need for this kind of behaviour on or off the court and I hope the governing body of this sport does not stand for this and stands up for the integrity of the sport that we have worked so hard to build."
Kyrgios said he spoke with Wawrinka after the match.
"I told him I was sorry," Kyrgios said Thursday. "Obviously he was angry. So I just had to deal with it. Something I had to deal with. Hopefully we can just put it behind."
Kyrgios also issued an apology on his Facebook page.
"My comments were made in the heat of the moment and were unacceptable on many levels," Kyrgios wrote. "I take full responsibility for my actions and regret what happened."
Tennis Australia said in a statement that it noted Kyrgios "has apologized to all involved for his comments on court in Montreal yesterday and deeply regrets his actions. ... Tennis Australia is working closely with Nick and his team to provide the best possible support; we understand how important it is to help educate and influence him both on and off the court."
The fifth-ranked Wawrinka announced in April that he had separated from his wife, with whom he has a daughter. The 30-year-old Swiss player has since been linked with 19-year-old Donna Vekic of Croatia, who is ranked 127th.
Vekic played mixed doubles with Kokkinakis, also 19 and ranked No. 76, at the 2014 Australian Open as a wild-card entry.
Kyrgios, 20, beat Wawrinka on Wednesday when the Swiss retired with a lower-back injury while trailing 4-0 in the third set.
In a postmatch interview on court, Kyrgios said Wawrinka had provoked him.
"He was getting a bit lippy at me so, I don't know, it's just in-the-moment sort of stuff," Kyrgios said. "I don't really know. I just said it."
Wawrinka's coach Magnus Norman also tweeted criticism about Kyrgios, who has been at the center of controversy in recent weeks.
At Wimbledon, Kyrgios battled with umpires time and again, was accused of tanking -- appearing to make little attempt to return a serve during a fourth-round loss to Richard Gasquet -- and swore so loudly and abused his rackets so violently that he was fined nearly $10,000.
Australian swimming great Dawn Fraser said she was disgusted with Kyrgios' behavior at Wimbledon, telling a breakfast television show that he "should be setting a better example for the younger generation of this great country of ours" and that he should go back to where his parents came from.
Kyrgios, who was born in Australia to a father born in Greece and mother born in Malaysia, replied on Twitter that Fraser was a "blatant racist." She later apologized.
The Associated Press contributed to this report.