The bill is now likely to reach 6bn euros (£3.9bn), George Alogoskoufis told a parliamentary committee.
The original budget for the Games was 4.6bn euros, but Mr Alogoskoufis admits "there will be significant overruns".
Preparations for the games have been beset by problems with construction delays and the pressures of shouldering a massive security operation.
George Alogoskoufis, Greek finance minister
Some 995m euros has already been spent on making the Games safe.
Mr Alogoskoufis warned that the overspending had reached such a level that Greece's budget deficit was likely to spiral.
"I have to warn you there will be deviations from the 2004 budget and it will be hard to keep the deficit under 3% of GDP," he told parliament.
IOC criticism
Greece is a member of the European Union and, under the bloc's rules, all members are expected to ensure that their deficits remain below 3% of GDP.
The European Commission has already criticised Greece over this, and is keeping a close watch on the country's finances. It is expected to issue recommendations on how Greece can combat its deficit on 24 June.
The Greek authorities have also been accused of exacerbating the delays through bureaucratic in-fighting and criticised for overly ambitious and lavish plans.
One fixture which has been particularly criticised is the complicated main stadium roof, which cost a mammoth 189m euros to build and was only fitted a few weeks ago.
In a recent interview with Belgian newspaper Le Soir, the president of the International Olympic Committee, Jacques Rogge, criticised the glass and steel roof and said that in future the IOC would choose cities that "already have a maximum of infrastructure in place and a minimum of virtual plans".
Strike threat
Now the organisers are in a race against time to complete the competition venues in time, but they are facing threats of industrial action from state workers.
Last minute cost-cutting measures instituted by the organisers mean that a bonus promised to civil servants and the emergency services for their extra efforts will now not be paid.
According to reports in the Greek media, a government minister said only security personnel would be paid the bonus.
In response public sector union leaders are threatening to strike, even during the Games, if necessary.
Greece has ordered all government agencies, including health and transport services, to be fully staffed throughout the event.
