"Kokkinakis banged your girlfriend," Kyrgios was caught saying by television cameras in reference to his Davis Cup team mate Thanasi Kokkinakis. "Sorry to tell you that, mate."
Wawrinka, who separated from his wife last year, has been linked with Croatia's WTA Tour player Donna Vekic, as has Kokinakkis.
It was unclear if Wawrinka heard the insult during the match as he shook hands with Kyrgios after he withdrew with a back injury while trailling 4-0 in the third set though his coach Magnus Norman criticised the Australian on Twitter afterwards.
"That was really really low Nick Kyrgios," Norman wrote. "Hope for u that u have people around that will teach u a thing or 2 about life tonight. Very bad."
Kyrgios said after he had won the second round match 6-7(8) 6-3 4-0, that he had been responding to an insult from the two-time grand slam champion.
"He was getting a bit lippy with me," Kyrgios said of Wawrinka. "Kind of in the heat of the moment. I don't know. I just said it."
A video from Wawrinka's press conference at the tournament later appeared on video-sharing website You Tube.
"It's not the first time that he has big problems on court in terms of what he says and in terms how he acts," Wawrinka said in French.
"I just hope the ATP will take big measures against him because he is young, maybe but there's no excuse. 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 towards the people around, the other players, the ball kids, the umpires.
"I really hope the ATP will take major action against him this time."
Wawrinka added that he had confronted Kyrgios in the locker room, though the 20-year-old had attempted to avoid him.
"It will stay in the locker room," he said when asked what had said to the Australian.
"But I think 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."
Kyrgios may have lost fans over the sledge, with many criticising him on social media.
But some defended the tennis star.
(Writing by Jahmal Corner in Los Angeles; Editing by Greg Stutchbury)
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