Public Health Wales said there were three different infectious parties on the TUI flight 6215 on Tuesday, so all travellers on board are deemed “close contacts”.
TUI said it had contacted all 193 passengers and crew about self-isolating. The airline requires customers to wear face masks for the duration of the flight.
The party island is a popular destination with British holidaymakers and is also called Zakynthos.
It comes days after officials in Plymouth, Devon, launched an urgent bid to trace a group of 30 teenagers who returned from Zante after at least 11 positive cases.
Urgent call to holidaymakers
Greece and its popular holiday islands are currently exempt from the UK Government’s quarantine rules.
Dr Giri Shankar, of Public Health Wales, said: “These passengers will be contacted shortly, but meanwhile, they must self-isolate at home as they may become infectious, even without developing symptoms. Anyone with symptoms should book a test without delay.
“Our investigations into a number of cases of Coronavirus have indicated that a lack of social distancing, in particular by a minority of the 20-30 year age group, has resulted in the spread of the virus to other groups of people.
“I would make a direct appeal to young people to remember that even if they feel that they would not be badly affected by Covid-19 if they were to test positive for it, if they were to pass it on to older or more vulnerable family members, friends or colleagues it could be extremely serious, even fatal.”
Zante tightens lockdown
On Friday, authorities in Zante tightened coronavirus curbs to ban all gatherings of more than nine people in public or private, limited numbers allowed at a single table in restaurants to four – or six if they are first-degree relatives – and enforce mandatory face masks indoors and outdoors.