The suspects reportedly admitted to stealing thousands of dogs since the beginning of this year, claiming they weighed around 100 tons in all.
Le Thi Phuong, 34, Tran Van Thang, 33, and Lai Khac, 38, identified as the kingpins of the gang, and the other 13 would remain in custody for three months, police said Tuesday.
According to the police, the gangsters rode motorbikes through residential areas late at night with stun guns and caught dogs roaming on the street.
The police seized 51 dogs from them and informed the public earlier this month, asking families who lost pets to come and claim them.
More than 30 of the dogs had been returned to their owners as of Monday, and the police will temporarily take care of the rest before sending unclaimed ones to a dog rescue center for adoption.
The Asia Canine Protection Alliance provided medical treatment to the rescued dogs.
Vietnam consumes an estimated five million dogs a year, second only to China's 20 million.
A number of reports have said that many dogs cooked at restaurants are stolen pets sold to small, unregulated abattoirs.