The team left Tuesday night, traveling to India through the UAE.
The pandemic forced the team to reduce its number to three shooters, Tran Quoc Cuong, Nguyen Dinh Thanh and Phan Xuan Chuyen, and they are accompanied by South Korean advisor Park Chung-gun.
They have not received Covid-19 vaccines, but all tested negative 72 hours before arriving in India. They will be tested again on arrival and isolated if found infected.
Tran Quoc Cuong, 47, is the star of the team. He is ranked 17th in the world by ISSF, and will win Olympic berths if he moves up one place and enters the top 16.
Coach Nguyen Thi Nhung said: "Cuong's performance has been very steady. The preparations were planned carefully.
"However, he will be under great pressure because this is the last opportunity for him to qualify for the 2021 Summer Olympics."
He has taken part in nine SEA Games since 2001 and won dozens of team and individual gold medals. He attended 2016 Rio Olympics and was part of teams that won Vietnam three bronze medals at Asian Games.
More than 300 shooters from 43 countries are set to compete in rifle, pistol and shotgun events in New Delhi.
The Vietnamese team is expected to finish on March 22, but will have to wait for 10 days for a flight home. Upon return, they will be quarantined for 14 days.
Only five Vietnamese athletes - two archers and a boxer, swimmer and gymnast each - have so far qualified for the Olympics against a target of 20.
The 2021 Tokyo Olympics will begin on July 23 regardless of the pandemic situation.