The latest confirmed cases were on the same flight from Wuhan, China, to Vietnam and had close contact with three previous patients detected on Jan 30.
The cases are currently limited to four provinces out of 63 in Vietnam.
On Saturday, Vietnam declared a public health emergency over the coronavirus epidemic and said it would halt all flights to and from mainland China.
Vietnam Airlines on Friday said it would cut flights between Ho Chi Minh City and Hong Kong to seven from 10 per week.
The Vietnam government also advised its citizens to limit large gatherings. Trade and exchanges with China are discouraged during this time.
The total number of coronavirus infections in China passed 17,200 on Monday while the national death toll hit 361, exceeding the 349 mainland fatalities from the 2002-2003 severe acute respiratory syndrome (SARS) outbreak.
The numbers came a day after the first death outside the country was reported in the Philippines. The fatality is a Chinese man from the city of Wuhan, where the virus was first detected.
The 44-year-old man had arrived in the Philippines with a Chinese woman who had also tested positive for the virus.