A Vietravel Airlines spokesperson said the carrier started selling air tickets for the routes on Friday, with one-way tickets costing from VND660,000 ($26.61).
There would be daily flights on each of the routes.
Vu Duc Bien, general director of the carrier, said Thailand is one of its key markets in Southeast Asia.
"After nearly two years of operating domestic routes with more than 6,000 flights connecting major tourist cities in Vietnam, it's time for the carrier to enter the international market as international tourism gradually recovers," he added.
Both Vietnam and Thailand reopened their borders to foreign tourists and lifted most Covid restrictions.
Thailand was Vietnam's fastest growing tourist market before the pandemic, with the number of visitors from that country rising by 46% year-on-year to 509,000 in 2019.