The flights comprise EK392 from Dubai to Ho Chi Minh City on March 12, and BR395 from Taiwan (China) to HCM City on March 16.
The ministry asked all the passengers on the flights to contact disease control centres of cities and provinces for guidance on health monitoring.
Airline ticket agents are responsible for notifying the passengers who bought tickets for those flights.
Besides, passengers who were on flight TG917 from London to Bangkok on March 15 and took a transit flight to Vietnam will also need to contact the municipal and provincial disease control centres, the ministry said.
Eight other flights with passengers on board contracting COVID-19 were announced by the ministry on March 16.
The number of COVID-19 cases in Vietnam stands at 66 now, 16 of them have been discharged from hospital following their full recovery.