The ambulance rolled on Port Wakefield Road about 2:45am at Virginia, north of Adelaide.
The female patient from Port Pirie, who was travelling in the rear of the vehicle, died at the scene.
Police said the woman’s 16-year-old daughter was also inside the ambulance at the time and was taken to the Royal Adelaide Hospital where she is in a stable condition.
The driver is a 38-year-old man from Adelaide’s western suburbs.
Police said he had been reported for causing death by dangerous driving and would appear in court at a later date.
Ambulance Employees Association of SA secretary Phil Palmer said he had spoken with the paramedic driver and believed he had done nothing wrong.
He said the crew was on a 12-hour overnight shift.
“Ambos are there to save lives and when something like this happens, it’s the worst nightmare, not just of this particular crew, but of the whole ambulance service,” Mr Palmer said.
SA Police Inspector Ben Spender earlier said there were no other vehicles involved in the crash and the ambulance was not in emergency mode at the time.
“It’s not my understanding that there was any time-critical risk or emergency transport,” he said.
The ambulance was one of two bariatric ambulances in the service’s fleet, which carry additional equipment to move larger patients.