The Ministry of Agriculture and Rural Development (MARD) culled more than 130 sick pigs and sprayed the infected areas.
Hưng Yên Province has set up quarantine stations to manage culling, transport and trade.
Samples have been taken for testing in those areas.
Similar measures were taken in Đông Đô Commune, Hưng Hà District of Thái Bình Province.
ASF was discovered in China in August 3 last year and has resulted in the termination of 950,000 pigs. There is no specific remedy or vaccine for the disease.
Phạm Văn Đông, director of the Department of Animal Health, warned that breeders should clean cages regularly, spray disinfectant and prevent insects because they could spread the disease.
Breeders should not buy piglets without knowing where they are from or transport animals suspected of having the disease.
Đông said theses were isolated outbreaks so farmers should not be too concerned, but should take preventive measures.
ASF cannot be transmitted to other animals or humans so customers should not turn their backs on the meat. They should just choose products with clear origins, he said.