"Greece's exit from the euro is not something that is part of our plans, simply because we believe it is like building a house of cards. If you take out the Greek card, the others will collapse," Varoufakis said in an interview with Italian public broadcaster Rai that was aired on Sunday.
Varoufakis also incurred the wrath of his Italian counterpart Pier Carlo Padoan by comparing Italy's problem with its large public debt to those of Greece.
"Italian officials… have approached me to say they are supportive of us but that they cannot tell the truth both because Italy risks bankruptcy and they fear the consequences with Germany," he said.
"A cloud of fear has hung over Europe in recent years. We have become worse than the former Soviet Union."
Padoan responded with a tweet calling Varoufakis's remarks misplaced and insisting that Italy's debt was "manageable."
Italy's debt mountain represents just over 130 percent of GDP, compared to 175 percent for Greece.
Quizzed by Italian reporters attending the G20 meeting in Istanbul on Monday, Padoan played down the clash.
"We have had a chat about it and exchanged some messages. There is no problem, and even less so on a personal level," Padoan said.
"Italy's objective is to find a shared solution to Greece's situation, starting with the eurogroup meeting in Brussels on Wednesday," he was quoted as saying by the AGI news agency.
"The European institutions are very open to finding a solution in everybody's interest. For the moment there is no plan B. Before anything else we must see what plan A is."