“The goal is the universal and complete vaccination of the permanent residents of the islands by the end of June at the latest,” he told a news conference.
Some 700,000 residents are involved in the plan, reports local media.
Islanders will receive the Johnson & Johnson vaccine, which only requires one dose.
The vaccination programme aims to build “the first massive wall of immunity” in Greece, Mr Mitsotakis said.
Greece has indicated it will welcome British tourists from 14 May, as it aims to get its battered tourism industry back on its feet following a year of Covid travel restrictions.
Britons are allowed to travel internationally for leisure from 17 May, although to a slender list of “safe” countries, which currently does not include Greece.
Greece has a “very good status”, according to the Greek tourism minister.
“We consider Greece is at a very good status regarding the epidemic at the moment and every week it is getting better and better. This is what the data shows,” said Harry Theocharis.
He added that the UK could have taken a “different approach” for the islands, where residents are being vaccinated as a priority.
While UK transport secretary Grant Shapps has said that he would be willing to adopt the “islands approach” introduced last summer, where certain islands were given a travel corridor, the first inclusions on the green list don’t include islands.