Nicknamed Little Mermaid for her swimming achivements, Vien, 23, finished the women's 400 meter Individual Medley race in four minutes and 44.62 seconds.
The gold medal was won by French Lesaffre Fantine with the time of four minutes 37.91 seconds, and the bronze by China's Yang Chang with four minutes and 46.77 seconds.
With her award, Vien, a captain in the Vietnamese army, bagged the first medal for Vietnam at the army sports event being held October 18-27 in Wuhan, the capital of central China's Hubei Province.
She will also take part in the 200m, 800m freestyle, 100m backstroke and 200m medley.
At the previous Military World Games in 2015, Vien won a gold medal in the women's 200m medley, one silver in the 800m freestyle and a bronze in the 200m backstroke.
The Military World Games is a multi-sports event held every four years since 1995.
This year, Vietnam sent 32 athletes to compete in seven sports: swimming, boxing, badminton, shooting, wrestling, track and field, and artistic gymnastics.