In a heated exchange with CNBC Anchor Julia Chatterley, he was asked whether he felt he was a liability to his government as the photo shoot might harm his efforts to promote a serious message about Greece's dire financial straits.
"Are you a liability for your channel?," he asked CNBC's Chatterley, before saying that he "tried not to be."
The Greek Finance Minister then walked out of the CNBC interview.
Dimitris Papadimoulis, member of the European Parliament for the Syriza Party, weighed in to the social media storm that has erupted since the Paris Match article.
On his Twitter page over the weekend he posted a request for the party to do "less interviews" and "more work," adding that the current situation called for "serious solutions."
The heads of the Syriza Party have also been accused of backtracking on the mandate they were elected on - namely reducing the amount of austerity Greek citizens are facing.
Athens needs to agree on a revised package of measures, despite being given the green light for a four-month extension to its current bailout program.
Varoufakis rebutted these accusations to CNBC, saying the government had not implied that it would renege on any promises.
"We said that our promises concern a full-year parliamentary term. They'll be spaced out in an optimal way and in a way that is in tune with our bargaining stance in Europe and also with the fiscal position of the Greek state," he told CNBC at the Italian event.
"This is what a responsible government does, it's what we were always were going to do. We have already started legislating for the humanitarian crisis, we are in the process of legislating for tax evaders, we will legislate on minimum wages in good time after deliberation with social partners which we always promised to do."
He criticized the press for "concocting stories" and added that the Greek government now needed "peace and quiet" in order to get "down to work to put Greece on the path of recovery."
At the conference, Varoufakis told reporters that he was confident an agreement would be reached with the country's creditors by April 20.