The proposal signed by municipal People's Committee Chairman Nguyen Thanh Phong was sent to the government on February 20.
According to the committee, the shutdown needs to be applied for schools of all levels in the city.
Under the recommendation, the national high school graduation of this school year should be changed to July.
The committee said that the further school closure is aimed to ensure safety for students as the coronavirus still poses a risk.
HCM City was the first locality to decide local students should stay at home until the end of February.
Vietnam gradually developed an effective treatment plan for coronavirus patients with 15 out of 16 infected cases successfully treated, the Ministry of Health reported.
However, the country still has 34 unconfirmed cases and more than 1,530 people in close contact with people who may have the virus or those arriving from epidemic areas.