Much of the focus so far in rehabilitating Greece has focused on the scale of its national debt, which is approaching double its economic output.
In comments to an Italian newspaper published on Saturday, ECB president Mario Draghi said that some debt relief may be required.
But the tests throw the spotlight on personal debt.
Banks have struggled most amid the months-long stand-off between leftist Prime Minister Alexis Tsipras and his country's international backers - the International Monetary Fund and European Union.
The dispute led to the freezing of central-bank funding for Greece's banks and forced controls on cash withdrawals. Although this stemmed a further hemorrhaging of savings, it squeezed the economy, making it harder for borrowers to repay loans.