"The movement of sheep and goats for breeding, fattening and slaughter is banned throughout the country," the ministry said in a statement.
It said its veterinarians had detected sheep and goat plague in the Corinth and Larissa areas after tracing the route followed by animals imported from a particular country.
The sick animals were found before symptoms of the disease appeared, the ministry said.
The country of origin was not specified, but the ministry said Greece imported sheep and goats mainly from Romania, Turkey and Albania.
More than 9,000 animals have already been earmarked for culling. 7,000 of them have been culled in central Greece after the disease initially appeared near the town of Kalabaka on 11 July.
Last week a senior veterinary official in the area was replaced after it emerged that some of the sheep had been buried alive, the local governor said.
The disease, known as Peste des Petits Ruminants (PPR), is highly contagious in sheep and goats but does not affect humans. Meat and pasteurised milk are also safe to eat, officials said.
The Greek agriculture ministry said the disease was detected for the first time in the country.
Greek farmers have increased imports of livestock after local herds were wiped out by last year's catastrophic floods caused by Storm Daniel. Tens of thousands of sheep died then. | BGNES