In a directive it issued on Monday the ministry said cities and provinces must monitor all Covid outbreaks and have response measures ready.
The World Health Organization classified EG.5 as a "variant under monitoring" on July 19 after a surge in incidence since early July. It has been increasingly reported across the globe, particularly in Asia.
On August 9 it was upgraded to a "variant of interest."
This follows the rise of another variant, EG.5.1, known as Eris.
EG.5 has so far been reported in more than 50 countries.
According to WHO, during the week ending July 23, the global prevalence of EG.5 was 17.4% of all Covid cases.
"This is a notable rise from the data reported four weeks prior, when the global prevalence of EG.5 was 7.6%."
There is no evidence yet that EG.5.1 causes more severe illness than other Omicron variants, and has similar symptoms.
Tran Dac Phu, senior advisor to the Public Health Emergency Operations Center, said Vietnam should closely monitor information about the prevalence and virulence of all new variants, including EG.5.
In the meantime, people should continue to wear masks in areas with high infection risk such as closed and crowded spaces, get vaccines and boosters, and disinfect hands regularly, he added.