Wales Health Minister Vaughan Gething said there are six case groups, or 30 infections, related to flights from the Greek island.
Passengers arriving on a TUI flight from Zante to Cardiff on Tuesday night were presented with Covid evidence.
TUI also stops at the beach hotel of Isla Laganas, as the social distance is ignored.
This comes after at least 16 other people tested positive on a TUI flight from Zante to Cardiff Airport last week, where some passengers said they did not adhere to Covid-19 rules.
Passengers arriving at 22:40 BST from Zante on Tuesday, operated through TUI, won a letter asking them to isolate themselves before leaving the airport.
You will also be presented with two Covid tests – one in 48 hours and in 8 days
The flight was already in flight when the Welsh government made the announcement.
Travellers from Wales arriving from other UK airports from the island, for example Cardiff arriving at Bristol Airport, on Tuesday and Wednesday are invited to organise tests on their return home and in 8 days.
They are told to isolate themselves.
Meanwhile, the Scottish government has announced that all other people arriving from Greece will be invited to quarantine for 14 days from Thursday.
In a statement, Gething said that lately there were “six teams representing more than 30 instances last week of 4 flights, two of which landed in England. “
He said there were several examples of positive travellers to Covid-19 who had moved away when they returned to Wales.
Gething called for a “quick meeting with the UK government and decentralised nations” to talk about converting regulations so that Greece’s travellers are forced to isolate themselves.
His comments came shortly after the Scottish government announced its decision.
“Public Health Wales has expressed direct considerations about public fitness posed by passengers returning to Cardiff tonight from Zante/Zakynthos. Percentage of that concern,” he said.
“It is almost certain that travellers returning to Wales from spaces with the highest incidence of Covid-19 will cause additional outbreaks of infection in Wales. Travelling to Wales from continental Europe led to the first wave of Covid-19. “
Andrew Flintham, executive leader of TUI UK and Ireland, said the holiday in Laganas, which attract teams from other young people, will no longer be available from Thursday.
“Recent cases show that some consumers respect Covid’s social estating and security measures,” he said.
“This is the right thing to do to protect and reduce a potential threat now known to others by not offering any more vacations at this specific resort.
“Recent cases in Wales have highlighted a population of customers who recently returned from Zante and tested positive.
“As an airline flying between Cardiff and Zante, it has allowed us to perceive trends that can also be seen in other parts of the UK. “
Some passengers on the flight to Cardiff last Tuesday said they had to isolate themselves before learning of the positive case after claiming the regulations were broken.
Stephanie Whitfield said the boy next to her had a “mask around her neck” and that “people would take off their masks and walk down the aisles talking to others. “
But Barry’s Nigel Harris, who on the plane told Jason Mohammed of BBC Radio Wales that the return flight was a “quite popular flight” and that he did not see other people get on and off the plane.
“I had my mask from the moment I left the hotel until I left Cardiff Airport and, in my experience, that’s also what I saw on the plane,” he said.
Mr. Harris said that regulations were being enforced and that several tannoy announcements had been made to remind people.
TUI said in response: “After an initial investigation with our cabin crew, we are confident that several advertisements through APs and individual conversations with consumers to verify protocols have taken position and that other consumers on the flight have shown that those findings are correct. “