This is the first medal for Vietnam at the largest regional sport event.
Oanh got 142 points in total, behind her Indonesian rival Sri Ranti with 144 points.
The Vietnamese archery team with 16 athletes vies for 10 sets of medals.
Vietnam will send more than 470 athletes to compete at the Games in Malaysia from August 19-31. They are scheduled to take part in 32 out of 38 sports and meet about 6,000 athletes from 10 other countries in the region.
At the previous games in Singapore in 2015, Vietnam finished third with 73 golds. Thailand (95 golds) and the hosts (84 golds) secured first and second positions, respectively.