Greek deputy civil protection minister Nikos Hardalias said Mykonos and Ios were “one step” away from authorities imposing restrictions amid a rise in Covid cases.
He also raised concerns for Zante, Tinos, Lefkada, Santorini, Paros and Rhodes.
All but essential travel has been discouraged to and from the country’s south Aegean islands after a surge in transmissions.
The region was marked dark red on the European Centre for Disease Prevention and Control’s (ECDC) Covid-19 map on Thursday.
In Italy, quarantine rules have been extended for British tourists for another month.
All Britons must show a negative Covid test result, quarantine for five days and test again at the end of their isolation period in order to enter Italy.
The country reported 6,171 infections and 19 deaths on Thursday, up from 5,696 infections and 15 deaths on Wednesday, according to its health ministry.
It comes despite the UK government’s recent decision to scrap quarantine for double jabbed arrivals from the US and the EU.
Greece, which depends heavily on tourism, had relied on promoting “Covid-free” islands to draw visitors back this summer after its worst summer in decades in 2020.
Britain and Germany are usually Greece’s biggest sources of visitors but Germany listed Greece as a coronavirus risk area this month after a surge in cases.
Mykonos, Santorini and Rhodes are the most popular tourist hotspots, drawing millions of people every summer.
But despite a strong June in terms of arrivals and optimism from ministers and tourism officials, uncertainty remains over how the season will unfold.
“We’re waiting to see how the (tourist) markets will react,” said Manolis Markopoulos, president of the hoteliers association of Rhodes.
The dark red zones on the ECDC map help distinguish very high-risk areas and also help EU member states uphold rules requiring testing on departure and quarantine upon return.
Last week the ECDC downgraded Crete, Greece’s biggest island and another popular destination, to the dark red zone.