The vaccines are prioritized for older people, and those under would get vaccinated once more doses are available, the Ministry of Health said.
Last month Prime Minister Pham Minh Chinh had urged the Ministry of Health and the Ministry of Education and Training to vaccinate students so that the new school year could begin safely.
Around 20 million students began the new year on Monday, with most schools holding their opening ceremonies online. They will attend online classes or study from televised lessons as the Covid outbreak continues unabated.
So far authorities have vaccinated over 22 million, with 3.3 million getting two shots.
The country aims to secure 150 million doses to vaccinate 70 percent of its 96 million population by next year.