The trio of Phan Xuan Chuyen, Phan Cong Minh and Lai Cong Minh finished third in the men's team 10m air pistol event at Daegu International Shooting Range.
Indian marksmen took the gold while the host athletes secured the silver.
Vietnam sent a team of six athletes and two coaches to the tournament, which closed on November 19.
They competed in the women's individual air rifle and men's individual and team air pistol events.
This is the first championship that will be counted towards the new Asian Ranking System.
The Vietnamese athletes will next take part in the Southeast Asian championship from December 1-10 in Thailand.