Since the end of March, this has only been allowed to permanent residents of the islands due to measures against the spread of the coronavirus.
According to Greek state television, the ferries will carry a maximum of 50 per cent of the number of passengers they were allowed to carry before.
Athens has already announced plans to restart tourism for foreigners. At the end of May, the Greek Crisis Staff plans to announce a list of countries from which tourists will be able to arrive without being subject to a two-week quarantine.
These will be countries with a relatively small number of infected, said Greek Tourism Minister Harris Theocharis.
He expressed hope that Germany, where most tourists traditionally come from Greece, would also be on the list. The first flights to Athens from abroad are expected to arrive on June 15. From July 1, all regional airports will be open for flights from abroad.