Vietnamese officials say they have carried out contact tracing measures in an effort to prevent additional spread of the virus.
A local English teacher was confirmed to have the virus on Monday, Vietnamese health officials said. On Tuesday, a 28-year-old woman and a one-year-old child were confirmed to be infected.
Local media reported the newly infected woman was a student of the English teacher. The young child had visited the teacher's house several times, the reports said.
The teacher, a 32-year-old man, had visited a Vietnam Airlines flight attendant who was quarantining at home following his return from Japan, Vietnam's VN Express website reported. The flight attendant tested positive for the virus on Saturday.
The flight attendant had been kept inside a quarantine area for five days before being released to self-quarantine at home.
Health Minister Nguyen Thanh Long said in a statement that the flight attendant "contracted the virus inside the quarantine area then spread it to others during his home-quarantine time."
The health minister said it was the first time such a transmission had happened. He added that the flight attendant "seriously violated quarantine regulations."
Health officials ordered 137 people who had been in close contact with the teacher to stay in a central quarantine center. They also closed the school where the man taught.
Vietnam's borders remain closed in an attempt to keep out the virus. Only limited international flights are operating to transport Vietnamese nationals and foreign diplomats and experts.
Prime Minister Nguyen Xuan Phuc has asked citizens and officials to strengthen measures to guard against continued spread of the virus. He said such steps are especially important ahead of the Communist Party's National Party Congress, which is expected to take place in early 2021.
"There will be many big gathering events ahead of the National Congress, our country's biggest political event, we can't let the virus affect us," the prime minister said.
Vietnam has reported 1,351 coronavirus cases, including 35 deaths. The Health Ministry has said nearly half of the confirmed cases were imported into the country.
The new cases ended Vietnam's 89-day stretch without any known local transmission of the virus. Earlier this year, it went 99 days without local transmissions until several new cases broke out in July. The outbreak happened at a hospital in Da Nang in central Vietnam.
I'm Bryan Lynn.