It said the distributed denial of service, or DDoS, attacks aimed at overwhelming the platform occurred for a second consecutive day on Tuesday.
The attack involved computers from 114 countries, causing outages and delays in high school exams but failing to cripple the system, the ministry said.
The cyber attacks prompted a judicial investigation ordered by a Supreme Court prosecutor, to be assisted by the police's cybercrime division.
"It is the most significant attack ever carried out against a Greek public or government organisation," the education ministry said, describing the incidents on Monday and Tuesday as "large scale and of sustained duration".
End-of year high school exams in Greece are administered using an online platform known as the Subject Bank, designed to to set a uniform standard across the country.
The outages left students waiting in classrooms for hours for the exams to start and touched off a political spat, following an inconclusive general election earlier this month.
A caretaker government has been appointed ahead of a new election on June 25, with the outgoing conservative New Democracy party favourite to win re-election.
"All we've got so far is an arrogant abdication of responsibility of the New Democracy government, which for four years failed to take adequate digital protection measures to shield the Subject Bank platform and ensure that school examinations run smoothly," Popi Tsananidou, a spokeswoman for the progressive main opposition party Syriza, said.
