Dozens of people have been forced into quarantine after South Australia reported two new coronavirus cases in travellers from interstate and a third in someone returning from overseas.

The cases take the number of active infections in SA to five.

The isolation requirements apply mostly to those people aboard three flights to Adelaide on Tuesday and Wednesday, two from Sydney and one from Melbourne.

A number of other exposure locations in Adelaide, including a southern suburbs supermarket, have been identified with SA Health expecting more to be added.

The two new cases from interstate involve a man in his 50s and a woman in her 20s who have been transferred to a quarantine facility.

Their close household contacts have also been placed in isolation.

The case in the overseas traveller involves a man in his 60s.

Thursday's cases also follow one revealed on Wednesday in a young Victorian girl who travelled from Nhill to visit relatives in Adelaide and tested positive after arriving in SA.

Following confirmation of the girl's infection, Chief Public Health Officer Nicola Spurrier said the family had decided to return to their home to quarantine.

The girl's grandparents, who live in Adelaide, have been vaccinated and will quarantine at home for seven days.

Professor Spurrier said the case showed there would be infections in SA with the relaxation of border rules.

"This should be a wake-up call for anybody who is not vaccinated. There is going to be COVID in our community," she said.

Under SA's new travel rules, anyone coming into the state must be double vaccinated and use a new online border entry process known as EntryCheck SA, which assesses an individual's vaccination status, departure location and COVID-19 risk.

Based on the information provided, travellers may also be prompted to use a new HealthCheck SA app, which will help them monitor daily symptoms and guide them through any testing and quarantine requirements.

In most cases, travellers are required to have a COVID-19 test within 72 hours of departure.

Unvaccinated travellers will be required to seek a special exemption with applications to be assessed on a case-by-case basis.