Premier Steven Marshall says the closure will apply from Friday with only returning SA residents, people permanently relocating to SA and essential travellers exempt from the new rules.
Returning residents or people relocating will still need to quarantine for 14 days.
A 100-kilometre buffer zone will also be put in place on each side of the SA-NSW border to allow cross-border residents free movements across the state line.
Marshall says the changes are in response to the latest health advice.
He says officials are also monitoring the situation in Victoria, where cases have just emerged, but no changes are planned at this stage.
The changes followed warnings on Wednesday from Police Commissioner Grant Stevens for anyone travelling from SA to NSW in coming days to “very seriously consider whether that travel is essential.”
He said South Australians on holiday or travelling in NSW should also consider returning home as soon as possible.
“The continued spread of cases in New South Wales is of particular concern,” a police statement said.
By Tim Dornin