Two villagers from the region's Zestaponi District became infected after contact with a sick cow.
"After putting the cow down, they discovered signs of the disease and buried the animal," the center's chief, Paata Imnadze, said. "Several days after, they were admitted to hospital with anthrax."
Both patients are currently in a stable condition.
According to the center, a total of 18 anthrax cases have been registered in Georgia this year. Last year the country saw 42 confirmed cases of the lethal disease.
Anthrax most commonly infects wild mammals and domestic cattle and sheep, which ingest or inhale the spores while grazing. Humans can be affected when exposed to blood and other tissues from infected animals. Anthrax spores can survive for long periods of time in the environment after their release.