Tour operator Tui has halted holidays to the resort of Laganas in Zante after customers failed to follow coronavirus safety measures.
The Scottish Government announced on Tuesday evening that travellers from Greece would have to self-isolate for 14 days from Thursday, while Wales also began asking arrivals from the island of Zante to quarantine.
The Department for Transport said no changes to its rules for England had been made, but Wales’ health minister Vaughan Gething said he would be pressing the UK Government for an urgent meeting to consider the potential risk in Greece.
Andrew Flintham, managing director of Tui UK and Ireland, said anyone who had booked to go Laganas after September 3 would be refunded for the cancellation.
Trips to all other resorts on Zante would continue as normal, he said.
"Laganas is a popular resort with young people who traditionally holiday in large groups of friends," Mr Flintham said.
"The health and safety of our colleagues and customers is our primary concern and recent cases shows that some customers are not following social distancing and Covid safety measures.
"It is therefore the right thing to do to protect and reduce a now identified potential risk to others by no longer offering holidays to this specific resort."
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Restrictions for Greece were lifted in England in July when international exemptions were first permitted.
There were 14.0 coronavirus cases per 100,000 people in Greece in the seven days to August 31, down from 14.9 a week earlier.
A seven-day rate of 20 is the threshold above which the UK Government considers triggering quarantine conditions.
Scottish Justice Secretary Humza Yousaf, announcing the restriction, said the "importations of new cases from Greece is a significant risk to public health".
He said "regular discussions continue" with the other three UK governments over restrictions.
Mr Gething said six clusters amounting to more than 30 cases of Covid-19 in the last week had come from four flights, two of which landed in England.
Greece’s tourism minister, Harry Theoharis, insisted the country is doing "everything in our power to ensure that every person that comes from the UK is kept safe".
He told BBC Radio 4’s Today programme: "We’re taking specific targeted measures where we see specific concentrations of cases. Measures that have been successful and have been working in the past few days."
He added that Greece has "a much lower number of infections compared to most other countries in Europe".
The Joint Biosecurity Centre was yet to change the risk rating for Greece but the data for the nation, like all others, was being kept under constant review.