Emergency services were called to the intersection of Jervois and Cumberland Sts about 10am after the crash.
A police spokeswoman said it was unclear what caused the truck to roll.
"It looks like it was carrying scrap metal, which has come out the back of the truck."
One parked car was shunted on to the footpath in the crash, knocking over a speed sign.
Firefighters helped manage traffic and clean up diesel spilling from the truck.
No-one was injured, a St John spokesman said.
The police spokeswoman said inquiries into the cause of the crash were ongoing.