Public Health Wales (PHW) is now contacting the remaining passengers.
It comes after a group of teenagers from Devon tested positive for the virus after a holiday on the Greek island.
On Sunday, PHW’s director of health Dr Giri Shankar said in a statement: “Cardiff and Vale test, trace, protect and Public Health Wales have identified at least seven confirmed cases of Covid-19 from three different parties who were infectious on Tui flight 6215 from Zante to Cardiff on 25 August.
“As a result, we are advising that all passengers on this flight are considered close contacts and must self-isolate.
“These passengers will be contacted shortly, but meanwhile, they must self-isolate at home as they may become infectious, even without developing symptoms.”
Dr Shankar added that “anyone with symptoms should book a test without delay”.
He also revealed that an investigation into positive cases in Wales had indicted a lack of social distancing between those aged between 20 and 30 had “resulted in the spread of the virus to other groups of people”.
The PHW director urged revellers enjoying the Bank Holiday weekend to remember the importance of social distancing.
“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,” he added.
It comes just days after health officials warned that up to 30 teenagers in Plymouth may be infected after holidaying in Zante.
At least 11 members of the group of 18 and 19-year-olds had already tested positive for Covid-19 as of Wednesday, officials said, as they warned residents to take precautions.
Some of the teenagers have since gone on a night out in the Devon city’s bars and restaurants, sparking fears of a wider outbreak.
Many of the teenagers who tested positive showed no symptoms or very minor symptoms such as a sore throat after returning from the Greek island.
Public health director Ruth Harrell said her team was working alongside the national systems to contact and trace the young people thought to have been affected.
“We know that some of these young people had no symptoms, and so carried on as normal, including a night out in Plymouth’s bars and restaurants, until they became aware of the risk,” she said.
“That means more people could be infected.
“While young people might have fairly mild symptoms, and sometimes none that you would notice, our big concern is that we know it can be very serious for people who have existing health problems or are older.”
Neither the Greek island, nor the mainland, are currently on the Government’s quarantine list, meaning that under normal circumstances passengers are not required to self-isolate.