In 2015 Vietnam had granted visa exemption for five years for Korean-Vietnamese, Italian-Vietnamese, and their spouses and children.
Vietnam has also suspended the 15-day visa waivers it offers all South Korean and Italian nationals.
The two countries are among coronavirus hotspots. South Korea has reported over 7,134 Covid-19 patients and 50 deaths, and Italy, 5,883 cases and 233 deaths.
Vietnam has reported 21 infection cases, with five diagnosed in the last three days after 22 days without a new case.
Nguyen Hong Nhung, 26, returning from Europe became Hanoi’s first Covid-19 patient Friday and the 17th nationwide. The 18th, 19th and 20th patients are a 27-year-old man returning from South Korea's Daegu City, the personal chauffeur and an aunt of Nhung.
The latest case, Vietnam's 21st patient, is a 61-year-old man on the same flight as of Nhung.
The government has ordered the aviation sector to limit flights to stricken areas to the extent possible.
It has also ordered the quarantining of everyone coming from South Korea, Iran, Italy, and mainland China for 14 days on arrival. In the case of arrivals from other countries, people from stricken areas are quarantined.
Starting Saturday, everyone arriving in Vietnam from overseas will need to fill in health declaration forms.
The global death toll from the Covid-19 epidemic has reached nearly 3,600 in 102 countries and territories, mostly in mainland China (3,097), followed by Italy (233), Iran (145) and South Korea (50).