The suspension takes effect from Wednesday and will last at least until the end of this month.
The Transport Ministry asked the Civil Aviation Administration of Vietnam to announce the suspension to all airlines in a bid to ease the pressure on overloaded quarantine facilities in the city.
Earlier, city officials had said that they expected to receive 17,000 Vietnamese coming home from abroad this week.
Earlier on Sunday, Vietnam suspended entry for all foreign nationals, including those of Vietnamese origin and family members with visa waivers.
Only Vietnamese nationals and foreigners having diplomatic and official passports such as business managers, experts and high-skilled workers will be allowed to enter the country at this time, and all entrants will be quarantined for 14 days.
Over the past few days, HCMC's Tan Son Nhat and Hanoi's Noi Bai airports, the largest in the country, have been receiving a large number of Vietnamese passengers returning home from foreign countries amidst escalating fears over the Covid-19 pandemic, overloading local quarantine facilities.
Nguyen Tan Binh, director of the HCMC Health Department, said the city has placed more than 7,000 people under centralized quarantine and around 1,000 at home.
On Monday, 27 flights landed at the Tan Son Nhat Airport and all passengers were sent to centralized quarantine areas.
Centralized isolation facilities in the city have around 23,800 beds and the city is calling for hotels and resorts to join the pandemic fight, serving as quarantine centers.
National flag carrier Vietnam Airlines has announced the suspension of all international flights starting March 25.
Other Vietnamese carriers have also suspended or cut the frequency of international flights.
Currently, only foreign airlines are transporting passengers into the country.
The country has recorded 107 new infections since March 6, with 106 still under treatment and one having recovered last week. 16 other patients were discharged last month after treatment. Of the active cases, 12 have tested negative either once or twice.
Many of the active cases are Vietnamese nationals returning from Europe and the U.S. and foreigners visiting from the same regions.
The Covid-19 pandemic has killed nearly 16,500 people, spreading to 195 countries and territories.