The lockdown, planned for six days, was to be lifted as of Sunday, although a range of measures were to remain to limit big crowds.
Saturday's case brought the latest cluster linked to a returned traveller from the UK to 26 infections. Officials said more cases over the next few days were likely.
"We are not out of the woods yet," South Australia Premier Steven Marshall said at a televised press conference.
Neighbouring Victoria, for months Australia's epicentre of the coronavirus pandemic, on Saturday posted its 22nd consecutive day of no new infections and no deaths. Victoria has recorded 90% of the country's 907 coronavirus-related deaths.
New South Wales, the most populous state where about a quarter of Australia's 24-million population lives, marked two weeks of no new coronavirus cases.
Compared to many developed nations, Australia has done far better containing the virus thanks to swift and strict measures. On Saturday, there were only around 93 cases active throughout the country.
Reuters