The three adults and one teenager are from four different households and have not travelled recently or had contact with a known case of coronavirus.
Contact tracers are now working to see if they are linked.
Director of public health Doctor Nicola Brink said she became aware of the possible cases at 4.30pm on Friday. Staff then resampled the individuals at their homes and at 7.30pm on Friday the positive results were confirmed.
The contact tracers then got to work.
'Through the evening until about one o'clock this morning we did the initial contact tracing,' Dr Brink said on Saturday.
'And it was apparent to us that none of the four individuals had travel history, nor did anyone have links to a case or contact with a traveller. So these really do appear to us to be unexplained community seeding, at the first sight.'
She said that at this stage they had not found a link between the four cases. They are all currently at home and in self isolation. The cases were picked up because the individuals were symptomatic, however none of them have lost their sense of smell or taste - one of the well-known symptoms of the illness.
'What we want to do now is not just look at the close contacts of those four cases... but also because we have developed an enhanced testing capacity, we will do far broader testing,' she said.
One of the individuals has an association with the Ship & Crown and the Crow's Nest.
'So we are asking everyone who was in the Ship & Crown or the Crow's Nest between 18th January and 20th January to contact us,' she said.
Contact should be made by emailing email@example.com and not by calling the helplines.
'What we also are doing, we will be personally contacting the parents of year eight at one of the schools on the island and we'll be asking all of those children to be tested, together with the teachers of those children,' she said.
'That will give us the first idea of what is going on.'
It was later confirmed the school involved was St Sampson's.
Dr Brink said they would also be contacting some retail outlets to do some targeted testing, as well as household contacts of the cases.
'We are expecting to do hundreds of tests over the weekend,' she said.
Dr Brink also urged islanders with any Covid symptoms to come forward to get tested.