Among bidders, there are big telecom firms like Vodafone from the UK and China Mobile from China.
The value of the license has not been revealed but is estimated to be over US$1.5 billion.
Besides, the license will be valid in 15 years.
At a recent meeting with the press, Tống Việt Trung, deputy general director of Viettel, said that the group spent a long period studying the Myanmar market and saw huge potential for mobile telecom development there.
Myanmar is one among few countries whose telecom market has yet to be tapped.
Telecom services in Myanmar have not been popular with high fees and low-quality infrastructure and telecom services.
A SIM card in Myanmar is priced at US$240-300.
According to Viettel, its revenues earned from telecom services overseas amounted to nearly US$600 million last year, with US$76 million remitted home, up 85% from the previous year.
This year, Viettel targets to achieve an overall growth of nearly 20% and a 50% growth in overseas markets.
The group has currently invested in seven overseas markets, comprising Cameroon, Cambodia, Laos, Haiti, Peru, Mozambique and Tanzania.
Apart from Viettel, MobiFone is the second telecom provider in Việt Nam to operate in Myanmar as it opened a representative office here last year.
However, MobiFone does not join the bidding in Myanmar, according to Việt Nam Post and Telecommunications Group, owner of MobiFone.