The move follows the hard closure of the border between the two states taking effect on Thursday.
Premier Steven Marshall says all people who have been to Victoria will be asked to present themselves for a test, regardless of whether they have symptoms or not.
Anybody returning to SA in the coming days will also be required to take a coronavirus test within 24 hours of their return and again on day 12.
They are also required to self-quarantine for two weeks.
Marshall says the surge in virus infections in Victoria is a “stark reminder of why we need to remain vigilant”.
“It’s a blunt reminder. We can’t rest on our laurels,” he said.
From Thursday, only people returning home from Victoria and essential travellers are allowed to cross into SA.
The new restrictions apply to everyone arriving by road or air, while people living in cross-border communities will be restricted to a 50km radius inside SA.
Police Commissioner Grant Stevens said maps were being produced to clearly show the entry limits and anyone from Victoria found breaching the rules could face a $1000 fine or further action.
People living near the border and needing to enter SA to conduct daily activities, such as attending school or for work, must have a pre-approved essential traveller exemption.
Stevens said additional resources would be deployed to border crossing points, with some smaller roads to be blocked.
SA police are also in discussions on the possible use of Australian Defence Force personnel to assist with the border lockdown.
South Australia reported no new virus cases on Thursday and no longer has any active infections.
More to come.
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