The child’s death is in addition to the death of a woman in her 90s this week who also contracted the virus.
The causes of their deaths are yet to be confirmed and have been referred to the coroner.
9News understands the little girl is from Adelaide’s western suburbs and is survived by her parents and three young siblings.
It is understood paramedics were called to their home in the middle of the night earlier this week.
However, SA Health could not confirm if the child had been in hospital or died at home.
The little girl is the sixth person to die in South Australia after testing positive for COVID-19 and the second in this current outbreak.
Premier Steven Marshall described the death of the child as “a tragic circumstance for the family”.
He said he can not go into further detail about the death.
“It’s a very sad set of circumstances but we still don’t know what the cause is,” Mr Marshall said.
“Obviously the family is in huge distress.”
Mr Marshall sent his condolences to the family.
The death comes as the state records 1374 new cases of the virus today.
Mr Marshall noted the latest infection numbers were a slight reduction on the number of cases that were reported yesterday and the day before.
“These numbers are very likely to be bobbing around for some time,” he said.
He said there were 23,420 processed yesterday in the 24 hours to midnight.
There are currently 37 people in hospital in SA with the virus.
Changes to close contact definition
The Premier announced the definition of a close contact will narrow as of midnight tonight, following an emergency meeting of National Cabinet.
“This will essentially be people who are household or intimate contacts with a positive case,” he said.
However, each state will look at “exceptions or exceptional circumstances in their state”.
“For example, in more vulnerable communities and also where there is a known significant transmission event,” Mr Marshall said.
“We might, if you like, flex up the definition of close contacts in a residential aged care facility because we know people there are far more vulnerable.
“Or if there have been multiple or a larger number of new cases or community transmission within an individual workplace, then we might have a larger definition of close contacts there.”
Mr Marshall said the time that both close contacts and positive cases should be in isolation in South Australia was also discussed.
“As of the next 24 to 48 hours we will be moving to 10 days for people who are COVID-positive and seven days for those people who are close contacts if they’re vaccinated,” he said.
“(This) will remain in 14 days if they’re unvaccinated.
“Ultimately if you don’t have any symptoms and you’ve done your 10 days… then you are right to go back to your business, obviously continuing to monitor any symptoms.”
The opposition leader Peter Malinauskas said the state government can’t sugarcoat the current situation.
“They were ready to let the virus in a controlled way, they had a COVID-ready plan and now all of those plans have gone to custard,” he said.
Mr Marshall said the states agreed to make a transition to more people using rapid antigen tests and “getting out of the line-ups for a PCR test”.
“Over the next 24 to 48 hours we’ll be looking at putting new directions in place to make it very clear to every single person in South Australia that we really want to test people that have symptoms, or are close contacts of those people that have symptoms,” he said.
“We will be significantly tightening up on that.”