Speaking to the Financial Times, the politician stated that a Greek default would be disastrous for the future of the eurozone, with the likely consequences being investors selling in other peripheral bond markets such as Ireland and Portugal.
"There are much broader implications for the eurozone should Greece have to restructure its debt," said Mr Papaconstantinou.
"People fail to see the costs to both Greece and the eurozone of a restructuring: the cost to its citizens, the cost to its access to markets."
He added that a default would lead to investment in other peripheral economies grinding to a halt and may result in a "fundamental break to the unity of the eurozone".
Mr Papaconstantinou said he believes Greece has two years to sort out its finances, with its â¬110 billion ($143 billion) loan bailout from the EU and the International Monetary Fund (IMF) set to expire in 2013.
He explained that the country will need to make up for the ending of the loans by building up a primary surplus and ensuring sustainable economic growth.
The politician said it will be a challenge to achieve the latter aim, but it is possible because the reforms introduced by the government have increased "growth potential".
However, Marco Annunziata, chief economist at UniCredit, said the markets are still unconvinced about whether Greece can avoid a default, because of the size of the cuts being demanded of the government.
Earlier this week, the IMF praised the current progress of the austerity program, noting that Greece is "on track" with its budget cuts for this year.
But it added that it will be important for the country to clamp down on tax evasion to help raise the revenues the state needs in the future, reported Reuters.
By Claire Archer