They were one of two people to die with the virus in the latest reporting period, along with a woman in her 80s.
"This was a young person that had other very severe health problems and in fact had been on a palliative care pathway," Chief Public Health Officer Nicola Spurrier told reporters on Friday.
"But because they did test positive for COVID, it will be counted as one of our COVID deaths."
Prof Spurrier said she understood the child had contracted the virus from a relative before testing positive at the Women's and Children's Hospital.
The child's family members are believed to have been fully vaccinated.
"Unfortunately for this little one, they were not old enough to be vaccinated," Prof Spurrier said.
"But by vaccinating ourselves we also protect those people that are more susceptible in our community."
About 57 per cent of children aged five to 11 in SA have been vaccinated, a figure Prof Spurrier described as being well below other age groups.
SA Health on Friday reported 5134 new infections, while the number of people in hospital fell slightly to 169 including seven in intensive care.
Public schools will no longer have to notify parents if there is a single case in their child's classroom in a bid to ease "burdensome" contact tracing pressures.
Instead they will notify parents if five children in a class test positive over the course of a week.
"The schools have been asked to (report) across year level and they are providing these very neat summaries of the number of cases across year levels," Prof Spurrier said.
"As a parent, I've found that very helpful."
Vaccine mandates for education and passenger transport workers have been scrapped as the state prepares for the eventual removal of the emergency management declaration.
But Prof Spurrier said healthcare and aged care workers would still need to be vaccinated and businesses could continue to enforce their own policies.
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