The orders affect around 200,000 students from kindergartens to universities in Hai Duong Province and over 300,000 in Quang Ninh, both in northern Vietnam.
The Ministry of Health on Thursday morning identified the two new patients as a 34-year-old woman working for Vietnam Poyun Electronics Co., Ltd. in Hai Duong and a 31-year-old man working at Van Don International Airport in Quang Ninh and living in Hong Ha Ward in Ha Long Town.
It is not known yet how the woman was infected, while the latter may have come into contact with Covid-19 patients arriving from abroad on repatriation flights.
Both are being treated at the National Hospital for Tropical Diseases in Hanoi.
Activities involving large crowds should be avoided and unnecessary meetings should be postponed, the Quang Ninh People's Committee said.
Vietnam has had 1,533 Covid-19 cases so far, 85 of them active, and 35 deaths.