The measure will come into force each month from 16 January. Anyone in that age group who is not vaccinated faces a 100 euro (£85) fine.
Greece becomes the second European country, after Austria, to make jabs mandatory.
Around two thirds of Greece’s population of about 11 million is fully vaccinated.
“We are focusing our efforts on protection of our fellow citizens and for this reason their vaccination will be mandatory from now on,” Greek Prime Minister Kyriakos Mitsotakis told a cabinet meeting on Tuesday.
Greece has recorded a spike in infections this month, with daily cases hitting record highs.
It has recorded 931,183 infections and 18,067 deaths since the start of the pandemic last year.
The country this month barred unvaccinated people from indoor spaces including restaurants, cinemas, museums and gyms, even if they had tested negative for the coronavirus.