The three men are: Nguyen Van Thuyen, 28, Nguyen Van Duyet, 25 and Nguyen Hong Cuong, 23, of Nghi Trung Commune, Nghi Loc District, Nghe An Province.
The woman is Luong Thi Bich Ngoc, 46, of Vinh Town. She is said to have bought the stolen dogs.
According to the police, the three men had committed the thefts from the beginning of June to the end of July.
They carried weapons including homemade guns and other "tools" to steal dogs belonging to residents of Nghe An and the neighboring province of Ha Tinh.
The normal modus operandi was for two men on a motorbike going around and using a stun gun on dogs found outside people’s homes. Accomplices in a pickup truck would follow and collect the unconscious dogs.
In instances where they were spotted by the locals and chased, they fought back and escaped, police said.
Authorities have seized several knives and swords and a pickup truck used to carry dogs from Ngoc’s residence.
Investigators have determined that the group carried out over 50 dog thefts, but not specified how many dogs were stolen and killed. They have only estimated the value of stolen dogs at over VND200 million.
Earlier reports have said Vietnam consumes an estimated five million dogs a year, second only to China's 20 million. Many dogs served at restaurants are stolen pets sold to small, unregulated abattoirs.