There will be biweekly flights from Singapore to HCMC on Mondays and Thursdays and one to Hanoi every Friday, the carrier announced on its website.
On January 1 Vietnam allowed the resumption of regular services to eight destinations, including Singapore.
Singaporean investors have been eyeing the Vietnamese market in recent years and around 12,000 Vietnamese live in Singapore.
Fully vaccinated people and those who have recovered from Covid-19 arriving in Vietnam only need to self-isolate for three days.
Everyone, except children below two, must have tested negative for the novel coronavirus using the PCR method within 72 hours before departure.
However, due to the emergence of the new Omicron variant of Covid-19, all passengers are also required to undergo a rapid test on landing at Noi Bai and Tan Son Nhat Airports, and pay $5 for it.