Travellers arriving home to Wales from Zante are being asked to self-isolate for 14 days.
Wales’ Health Minister Vaughan Gething said there are six clusters of cases, amounting to 30 infections, linked to flights from the Greek island.
All passengers arriving on a flight from Zante to Cardiff on Tuesday night will be offered two Covid tests – one in 48 hours and another in eight days.
Mr Gething said the passengers posed a public health risk.
It comes after at least 16 people tested positive following a TUI flight from Zante to Cardiff Airport last week, where some claimed passengers were not following Covid-19 rules.
Passengers on the 22:40 BST arrival from Zante on Tuesday, also operated by TUI, will be given a letter asking them to self-isolate before leaving the airport.
The flight was already in the air when the Welsh Government made the announcement.
Travellers from Wales who arrive from other UK airports from the island – for example, someone from Cardiff who arrives at Bristol Airport – on Tuesday and Wednesday are being asked to arrange tests when they arrive home, and again in eight days.
They are being told to self-isolate as well.
Meanwhile the Scottish government has announced that all people arriving from Greece will be asked to quarantine themselves for 14 days from Thursday.
In a statement, Mr Gething said there are currently “six clusters amounting to over 30 cases in the last week from four flights, of which two of these flights landed in England”.
He said there were several examples of Covid-19 positive travellers who had not self-isolated on return to Wales.
Mr Gething called for an “early meeting with the UK government and devolved nations” to discuss changing the rules so travellers from Greece are required to self-isolate.
His comments came just shortly after the Scottish government announced its decision.
“Public Health Wales have expressed direct concerns about the public health risk posed by passengers returning to Cardiff this evening from Zante/Zakynthos. I share that concern,” he said.
“It is almost certain that travellers returning to Wales from areas of higher Covid-19 incidence will lead to further seeding of infections within Wales. Travel into Wales from mainland Europe drove the first wave of Covid-19.”
Some passengers on the flight to Cardiff last Tuesday said they had decided to self-isolate before they even learned about the positive case after they claimed rules were being broken.
Stephanie Whitfield said the man next to her had a “mask around his neck” and “people were taking their masks off and wandering up and down the aisles to talk to others”.
But Nigel Harris, from Barry, who was on the plane, told BBC Radio Wales’ Jason Mohammed show the flight home was a “pretty standard flight” and he did not see people walking up and down the plane.
“I had my facemask on from the time I left the hotel to the time I left Cardiff Airport and, in my experience, that was what I saw on the plane as well,” he said.
Mr Harris said staff were enforcing the rules and a number of tannoy announcements were made reminding people.
TUI said: “Following an initial investigation with our cabin crew we are confident that multiple announcements via the PA and individual conversations with customers to try to reinforce protocols took place and other customers on the flight have confirmed these findings to be correct.”