Ebola test results for the pair are not yet known but the health ministry said their condition had improved.
"After 24 hours of monitoring, the two patients were without fever, showing no abnormal signs or symptoms related to Ebola," it said in a statement released late Wednesday.
The two men will be put under "community surveillance" for three weeks from the date they left the affected area, the ministry said.
Airline passengers sitting next to the pair -- who travelled to Vietnam on Monday from Nigeria via Qatar -- have also been advised to monitor their health conditions.
Vietnam has introduced mandatory temperature checks at its two major international airports in Hanoi and Ho Chi Minh City in a bid to prevent passengers bringing the deadly virus into the country.
According to the World Health Organisation, the latest official toll from Ebola has jumped 106 in two days to 1,350 dead, with the bulk of cases in Liberia, Guinea and Sierra Leone.
In Myanmar a local man is still undergoing tests after arriving from Guinea with a fever.