Calling for urgent preventive measures, the UN Food and Agriculture Organisation (FAO) said swine fever had become deeply entrenched in Georgia and had been reported in northern Armenia and the outskirts of the capital Yerevan.
"The spread of the African Swine Fever virus to the Caucasus region poses a very serious animal health risk and could lead to a dramatic situation," FAO Chief Veterinary Officer Joseph Domenech said in a statement.
"Without a more vigorous surveillance and disease control strategy the virus could become endemic in the Caucasus and could eventually make its way to other regions.
"The EU, Russia, the Ukraine and other countries have a serious problem on their doorsteps that needs to be urgently addressed," he added.
African swine fever is a highly contagious viral infection of pigs that is usually lethal but does not affect humans. It is endemic in most of sub-Saharan Africa.
The first case in the Caucasus was recorded in Georgia in June and has spread rapidly, affecting 52 of 65 districts while more than 68,000 pigs have died of the virus or been culled.
In Armenia, outbreaks are on the rise and it seems likely that the virus is spreading, the FAO said.
"If both countries do not get a grip on the virus, there is a real risk that they might lose most of their pig population," Domenech warned.
The statement said the FAO was planning to provide emergency technical assistance to Georgia and Armenia.