On-court microphones picked up the scurrilous sexual remark over Wawrinka's girlfriend by the 20-year-old Australian during a changeover at the Montreal Masters on Wednesday.
Kyrgios said that the woman had been involved with his close friend Thanasi Kokkinakis. "Sorry to tell you that mate," Kyrgios is heard to say.
Wawrinka reacted with fury.
"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 this sport that we have worked so hard to build," Wawrinka said in a Twitter statement after.
"So disappointing to see a fellow athlete and colleague be so disrespectful in a way I could never even imagine.
The comments were made after the first set which Kyrgios won 7-6 (10/8). Wawrinka won the second set 6-4, but withdrew with back problems when he was losing the third set 4-0.
At the stadium, Wawrinka, who has been linked to Croatian tour player Donna Vevic, said the Association of Tennis Professionals should take "major action this time" against Kyrios.
"It's not the first time that he has big problems on court in terms of what he says and in terms of how he acts. I hope the governing body does not stand for this."
Kyrgios, whose Twitter motto is "Play Your Own Rules", has been the target of criticism from the tennis establishment several times for his on-court behaviour. But Australian veteran Lleyton Hewitt began a mentoring role with Kyrgios that started in Montreal. Hewitt and Kyrgios were beaten in the first round of the doubles.
At Wimbledon, Kyrgios drew jeers from the public as he apparently did not bother to compete for a game in the second set of his fourth-round defeat by Richard Gasquet.
He also had problems with chair umpires on occasion during the fortnight. Kyrgios defended his action with Wawrinka after the match.
"He was getting a bit lippy with me. Kind of in the heat of the moment, I don't know, I just said it," said the Australian.
Wawrinka's coach Magnus Norman, said in a tweet: "That was really really low Nick Kyrgios. Hope for u that u have people around that will teach u a thing or 2 about life tonight. Very bad??"
Wawrinka said that he was not planning to comment further on the incident.
"It will stay in the locker room. But there are things, regardless of how you are, regardless of the stress you have on the court, there are things you just can't say. And regardless of whether he sidesteps it, I think the way he behaves on court he has big problems.
"Every match he has problems. Every match he behaves very badly.
"On top of that the problem is that he doesn't just behave badly towards himself he behaves badly toward the people around, the other players, the ball kids, the umpires.
"I really hope the ATP will take major action against him this time."