But SA will ease the statewide lockdown immediately to allow family groups to exercise, with stay-at-home orders to also be scrapped on Saturday.
Mr Marshall said investigations had revealed one of the close contacts linked to a positive case in a worker at an Adelaide pizza bar misled the contact tracing team.
The person had told authorities he had only purchased a pizza from the shop when in fact he had worked several shifts at the location.
"Their story didn't add up. We pursued them. We now know that they lied," Mr Marshall said.
"We are still trying to locate thousands of people who had dangerous contact at the Woodville pizza bar.
"Even more, now that we know this person lied, we have to find and isolate a whole new group of associates.
"To say that I am fuming about the actions of this individual is an absolute understatement.
The selfish actions of this individual have put our whole state in a very difficult situation.
Nevertheless, the premier said the move to lift the lockdown early would proceed, with SA largely moving to a one person to every four square metres density requirement.
The changes will allow most businesses to reopen from midnight on Saturday.