"Obviously, it's a tragic circumstance for the family."
Marshall said he was "not prepared" to say whether the child was being treated in hospital before their death.
"The family is obviously in a great deal of distress at the moment," he said.
The child is the sixth person with Covid-19 to die in South Australia since the start of the pandemic.
A Covid-positive woman, aged in her 90s, died in Adelaide on Sunday.
South Australia recorded 1374 new positive cases overnight, which was a slight reduction on Wednesday's numbers.
The Premier also revealed there were still 37 people in hospital, with four people in intensive care and one of them on a ventilator.
He urged people to get their booster shots.
"It still remains a massive logistical exercise to get so many people vaccinated in such a short period of time," the premier said.