A courtside microphone during ESPN's telecast picked up Kyrgios saying that Australian player Thanasi Kokkinakis had slept with a player who is reportedly Wawrinka's girlfriend.
Wawrinka tweeted Thursday that the Australian's words were "beyond belief" and that officials should look into the matter.
"So disappointing to see a fellow athlete and colleague be so disrespectful in a way I could never even imagine," Wawrinka 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."
The fifth-ranked Wawrinka announced in April that he had separated from his wife, with whom he has a daughter. The 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 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.''
The ATP rulebook allows a fine of up to $10,000 for incidents of verbal abuse or unsportsmanlike conduct.
The rules note that a "singularly egregious, a single violation of this section shall also constitute the player Major Offense of Aggravated Behavior.''
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 -- he appeared 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.