A total of 369 pigs have died from the virus so far in the province, including four on Sunday.
"Settlements where the disease has been registered... have a total of 9,000 pigs, all of which will have to be culled," the spokesman said.
Outbreaks of the highly contagious virus are rare outside Africa, but last spring, Georgia, which borders on North Ossetia, saw outbreaks in 10 regions. A total of 20,000 pigs were culled.
Preliminary reports said the infection may have been brought in by wild pigs. The virus can survive for up to 15 weeks in raw pork, and up to six months in processed meat. The virus, which causes lethal hemorrhagic disease in pigs, does not pose a threat to humans.
Around 170 people have been deployed to guard the province's border, to ensure that no pork products are taken out of North Ossetia.
At the time of the Georgian outbreak, the United Nations Food and Agriculture Organization warned of potentially severe consequences if the virus were to spread beyond the country's borders.