Wawrinka set up an all-Swiss semi-final with Roger Federer by beating Tsonga 7-6, 6-4, 6-3.
The Frenchman failed to attack Wawrinka's game enough to cause him any real problems but the pair clashed between games.
"What did you say?" Wawrinka said, after winning the first set.
Stan Wawrinka and Jo-Wilfried Tsonga appeared to have made up
"You’re the one looking at me and talking to me.
"What are you looking for? Come on, let it go. Did I look at you once?"
It is not the first time the two have come together.
After the Davis Cup final in 2014, the defeated French team and victorious Wawrinka clashed outside a bathroom during the official dinner, according to French newspaper L'Equipe.
However, both players brushed off the event as nothing more than heat of the moment.
“The beginning of the match was quite tense from both sides," Wawrinka said afterwards.
Stan Wawrinka kept his cool to progress through to an eighth Grand Slam semi-final
"You can always have some tension.
"Everybody goes out there to win, so things can happen.
“But at the end, there is no problem. We get on well."
Tsonga meanwhile seemed more nonplussed by events.
Jo-Wilfried Tsonga was unable to beat Stan Wawrinka on the day
“Sometimes it happens," Tsonga said.
"We say things during the game.
"But it was nothing special.
“We spoke about things that are between him and me.