Costas Tsiaras, the minister of agriculture and rural development, declared that the commercial killing of sheep and goats, as well as their movement for breeding purposes, would be prohibited nationwide.
The virus, commonly referred to as peste des petits ruminants (PPR), is extremely contagious and kills or severely sickens sheep and goats.
Although it does not harm people, it can kill up to 70% of sheep and goats who are affected.
In the hardest-hit central Thessaly region, about 7,000 animals in herds where the disease has been discovered have been slaughtered thus far.
Regional governor Dimitris Kouretas announced that 1,200 more people will be killed later this week.
The agriculture ministry stated in a statement that tightening security nationwide is deemed necessary for preventive reasons and is intended to limit the spread and eradicate the disease.
According to EU guidelines, if a case is found, the entire flock is killed, the afflicted farm is cleaned, and animals in the vicinity are screened for the illness.