Prime Minister Steven Marshall has confirmed that both people have underlying health issues.
One was in his 60s and the other in his 90s.
Mr Marshall added that although the number of cases had increased, he was pleased with the way residents of South Africa were handling the Omicron outbreak.
“We’re still in the 3,000 range, but we’re seeing an escalation in cases across the country,” Marshall said.
Several new vaccination clinics have opened statewide, with the Prime Minister announcing that 5,000 to 15,000 doses of the vaccine will be available each week from January 12.
On January 10, vaccines will be available for children aged 5 to 11 in South Australia and the rest of the country.
Demand for childhood vaccines exceeds supply
Mr Marshall expressed concern that the number of parents seeking immunizations for their children far exceeds the current supply of vaccines.
As a result, hundreds of appointments before the January 10 date have been canceled.
“What we are doing is taking every opportunity to get doses as soon as possible,” he said.
He said the allocation of vaccine doses South Australia receives is determined by the Commonwealth, with work underway to secure more vaccines.
“They stock up on immunization doses for 5 to 11 year olds just like they do for adults,” Marshall said.
He added that he could not yet provide for sure whether children would return to school or return to distance learning in the face of the Omicron outbreak.
Prof Nicola Spurrier, South Australia’s public health official, said the key to keeping children and school safe is to get vaccinated, especially if you are eligible for your third booster.
“As a pediatrician, school is so important to children. It is not just an educational institution, it supports their psychological development,” she said.
“We have worked a lot with education to make schools as safe as possible.
“We really want to increase immunizations in our state.”
Homes in Naracoorte and Robe
Ms Spurrier confirmed that there had been outbreaks of COVID-19 in remote areas of Naracoorte, near the Victorian border, and Robe, also to the south.
She added that more than 100 people had been infected at a slaughterhouse in Naracoorte, with SA Health working to provide RATs to affected workers.
RATs will also be available to residents in some locations, while the SA Police Commissioner was working to establish pickup points.
For eligible cardholders, RATs will be provided free of charge.