The restriction will be in place for 30 days and does not apply to those entering the country for state affairs or other special matters, the Ministry of Foreign Affairs said.
Vietnam has recorded 31 new infection cases over the past week, after discharging the previous 16 cases and going 22 days straight without new infection.
Eleven of the new patients are foreigners - 10 British and one Irish. Many of the remaining active patients are those who'd come from Europe or had contact with them.
The Vietnamese government's latest decision follows the World Health Organization (WHO) saying Europe is now the world's Covid-19 pandemic epicenter.
Vietnam will also suspend granting visas at border gates, the government has decided.
Foreigners who are experts, business managers and skilled workers wishing to enter Vietnam must undergo medical examination and follow anti-epidemic measures at enterprises and accommodation facilities in accordance with the Health Ministry’s regulations.
The Schengen area is a border control-free travel zone comprising 26 European countries, which are Austria, Belgium, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, and Switzerland.
Vietnam earlier halted visa waivers for citizens of eight European countries: Denmark, Norway, Finland, Sweden, Germany, France, Spain, and the U.K.
The country has also suspended its visa waiver for Italian nationals and South Korean nationals.
Starting March 7, everyone arriving in Vietnam from overseas will need to fill out health declaration forms and follow quarantine protocols if found carrying symptoms of the novel coronavirus.
President Donald Trump has suspended all travel from Europe to the U.S. for 30 days starting Friday, except for U.S. citizens and travelers from the U.K, in response to the rapid spread of the coronavirus.
The Covid-19 outbreak has thus far spread to 138 countries and territories around the world, with the death toll climbing to 5,400, including a record 250 deaths in one day reported in Italy.