The state has detected 36 cases since infections were found in Adelaide on Sunday, the first community cases detected in six months.
Authorities say the "circuit breaker" measures were necessary to stop the virus' spread "at the beginning".
Australia has previously also responded aggressively to small outbreaks.
Various state governments have at times closed parts of the economy, enforced border restrictions and other measures to stop the virus' spread.
The lockdown, to begin at midnight on Wednesday, comes just weeks after neighbouring state Victoria beat a second wave, which caused about 800 deaths.