Wawrinka withdrew from the match while down 0-4 in the third set, but not before Kyrgios' on-court claim that Kokkinakis slept with Wawrinka's girlfriend.
While walking to his seat having lost the first-set tiebreak, Kyrgios was heard saying: "Kokkinakis banged your girlfriend, sorry to tell you that mate."
The woman in question is believed to be 19-year-old Croatian player Donna Vekic, who Wawrinka was rumoured to be dating after separating from wife Ilham Vuilloud.
Kokkinakis had also been linked with Vekic after the pair played mixed doubles together at the 2014 Australian Open.
Kyrgios, playing his first tournament with Australian veteran Lleyton Hewitt as his mentor, won the second set 6-3 before Wawrinka retired in the third.
Wawrinka's coach Magnus Norman responded on Twitter expressing his disgust at the comment from Kyrgios.
After winning his first round match at Montreal, Kyrgios made it clear that Hewitt is not his coach but is mentoring both he and Kokkinakis.
Kyrgios is in Canada warming up for the US Open.
At his last major tournament at Wimbledon, little more than a month ago, the 20-year-old Canberran made headlines not for his unquestionable talent but due to his controversial antics on and off the court.
He argued with umpires and reporters and bowed out of Wimbledon accused of tanking when losing to Richard Gasquet in the fourth round.
Kyrgios returned to the limelight for Australia's Davis Cup tie against Kazakhstan in Darwin last month only to suffer a disappointing loss to 115th ranked Aleksandr Nedovyesov.
PHOTO: Nick Kyrgios delivered a brutal sledge to Stan Wawrinka during their match at the Montreal Masters. (Reuters/USA Today Sports: Eric Bolte )
