The latest case is someone who dined at a restaurant in Adelaide where previously infected people were also present on Saturday night.
The lockdown rules will come into effect from 6pm (local time), with South Australians only allowed out for five reasons.
Premier Steven Marshall said it had also been confirmed the current cases involved the Delta variant of the disease.
"We hate putting these restrictions in place but we have one chance to get this right. We are moving as quickly as we can to slow and stop the spread of this cluster.
"We know these restrictions will take a heavy toll. But we've always had a situation where we go hard and we go early in South Australia.
"We've got to stop movement around this state and we've got to stop it immediately."
South Australians will only be allowed out of their homes for essential care, essential work, the purchase of foods and essential goods, for medical reasons and for limited exercise.
The SA cluster began with an 81-year-old man who entered the country from Argentina, his daughter and another two men.
As the number of cases and exposure sites continued to grow, Marshall said more testing sites would open in Adelaide.
The outbreak has plunged thousands of people into quarantine with the list of more than a dozen exposure sites including at least four major shopping centres in Adelaide's north and northeastern suburbs.
That list was expected to grow further on Tuesday.
The elderly man had returned to Australia via New South Wales, where he spent 14 days in quarantine.
He returned to SA on July 8 and presented to a suburban hospital over the weekend after developing symptoms.
Business SA chief executive Martin Haese said the new restrictions were another blow to the already struggling hospitality, events, tourism and retail sectors.
"We hope there will be no extension to the restrictions beyond Friday."
NSW, Australia's most populous state of which Sydney is the capital, is in the fourth week of a five-week lockdown, battling the largest Covid-19 outbreak, with total cases exceeding 1400.
On Tuesday, NSW authorities reported a slight slowdown in new cases, reported 78 locally acquired ones, down from 98 a day earlier.
Meanwhile, a five-day snap lockdown in neighbouring state Victoria was due to end Tuesday night, but authorities said it would need to be extended for seven days.
Nine locally acquired cases were detected in Victoria from 13 a day earlier, in line with a downward trend and taking total cases to more than 80. Of the new cases, all but one was linked to the current outbreak, officials said.
Virus-exposed locations in Victoria have risen to more than 300 since the first cases were detected a week ago linked to a team of infectious furniture movers from Sydney.
- AAP and Reuters
