The site was taken offline until it was secure, she said.
Hackers involved with the loosely organized group Anonymous have been linked to attacks around the world aimed at punishing governments for policies they dislike or at showing that corporations' data security efforts are inadequate.
The hackers said they were protesting against the near-bankrupt country's bailout by the European Union and the International Monetary Fund which has been associated with unpopular austerity policies.
"You have joined the IMF against your people's acquiescence... democracy was given birth in your country but you have killed it," said a two-minute video in English which said it was from Anonymous and was posted on the ministry website.
Near-bankrupt Greece is currently locked in last-ditch talks with its creditors to stave off a chaotic default that might spill over to other euro zone countries.
(Reporting by Harry Papachristou; editing by Philippa Fletcher)