"I am unable to make good on my promises to the people to take the country out of crisis," Mirian Gogiashvili told reporters on Tuesday after meeting interim President Nino Burdzhanadze.
"I believe it is time to make way for new leaders."
Gogiashvili said Georgia was running a budget deficit of 255 million lari ($115 million).
Georgia's foreign debt stands at $1.75 billion. The average salary is just $20 a month and Georgia's new leaders are keen to attract foreign aid and investment to help the country out of its plight.
"We have to negotiate with those financial organisations like the International Monetary Fund (IMF), World Bank and also the European Union whose programmes were stopped under the previous government," said Roman Gotsiridze, head of parliament's budgetary office and a prominent economist on Monday.
The minister's resignation comes after a tumultous week in the Caucasian state after a determined opposition forced veteran President Eduard Shevardnadze to resign on Sunday.
Shevardnadze's fall came after three weeks of demonstrations against widely-criticised elections.