The shocked Canadian laughed, twirled and then covered her face with her hands before waving at the cheering audience.
Cohen made the request for a twirl after he noticed Bouchard had commented about Serena William's Australian Open outfit on Twitter.
"Last night you tweeted that you loved Serena's outfit. Obviously the fluoro is working for you girls at the moment. She was kind enough to give us a twirl, can you give us a twirl and tell us about your outfit," he said.
After twirling, Bouchard awkwardly noted: "I mean I have to say I think Serena's outfit is the best, even better than mine, I have to give her that."
The No. 7-ranked player, who described herself as a "perfectionist", later spoke about the unusual incident at a press conference, calling it "very unexpected."
"I don't know, an old guy asking you to twirl. It was funny," she added.
A Channel 7 spokesperson told Daily Mail Australia: "This interview did not air on Channel 7 or 7TWO.
Eugenie Bouchard celebrates her second round win. Photo / Getty Images
"Tennis Australia is the host broadcaster and provide a world feed to other broadcasters where this interview was picked up. Ian works for Tennis Australia."
Cohen was clearly holding a Channel 7 microphone and the interview appeared on Channel 7's sport website featuring their logo.
Bouchard has achieved the highest world ranking ever for a Canadian player and is considered the next big star in women's tennis.
She broke into the top 10 for the first time last year after reaching the finals at Wimbledon, where she lost to Petra Kvitova but became the first Canadian to appear in a Grand Slam final.
Bouchard has 25 wins and seven losses in majors and is playing in just her eighth Grand Slam event.
After the twirling incident, one shocked tennis fan on Twitter, Marsha Boyd, wrote: "We need more people to stand up against sexism. No one is asking @rogerfederer to twirl. Don't ask @geniebouchard!"
Val Andrea Way commented: "What the?? Would he have asked a Male pro tennis player to 'give us a twirl'?? How disrespectful and well pervy."
"Male presenter at @AustralianOpen asks professional female tennis player @geniebouchard after win to 'give us a twirl'. WTF?" Meg said on the social media site.
And Canadian journalist Signa Butler said: "Can we expect Federer to be asked same question? Pathetic. On-court presenter asks Eugenie Bouchard to 'twirl'."
Eugenie Bouchard of Canada takes a selfie after winning her second round match against Kiki Bertens. Photo / Getty Images
