Other measures come with requiring those arriving in the country by land borders, as well as those arriving from several European countries, to have evidence of a negative coronavirus test.
Verification must be carried out up to 72 hours before entering the country, and Greek citizens must also submit a verification.
All public occasions where other people stand, such as concerts and shows, are also suspended in the country.
Greece showed 126 new COVID-19s on the last day, bringing the overall to 5749.
Another virus-related death also raised the total number of deaths to 213 amid an increase in infections.
Seventeen of the new cases were migrants arriving on the Aegean island of Lesbos from the neighbouring Turkish coast.
On Monday, the Greek Ministry of Culture closed the Museum of Ancient Angora, a major archaeological site in central Athens, for two weeks after a cleaner operating there tested positive for the virus.
International coronavirus cases have exceeded 20 million and the number of reported virus deaths has increased to 736,191, according to Johns Hopkins University.
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About one-fifth of reported deaths, or more than 163,000, occurred in the United States, the highest in the world.
New Zealand Prime Minister Jacinda Ardern said Tuesday that four new cases of coronavirus had been shown in the country for the first time in 102 days.
Cases also continue to increase in several countries, with Indonesia and Japan.
It took approximately six months to succeed in 10 million international COVID-19 cases after the virus gave the impression in central China late last year, and just over six weeks for that number to double.
Russia announced tuesday that it had become the first country in the world to approve a coronavirus vaccine, experts have expressed doubts about its effectiveness.