All food and drink consumption must be while seated and dancing and singing remain banned.
Family gatherings will be limited to 10 people although weddings and funerals can have up to 50.
Schools will reopen on Wednesday and students will also be required to wear masks.
The new restrictions will remain in place for at least a week with the resumption of competitive sport delayed for a further week.
With no new cases, SA s Modbury cluster of coronavirus cases stands at 19 confirmed infections with 11 of those linked to the Tenafeate Creek winery near One Tree Hill.
It began with an 81-year-old man who recently arrived in Australia from Argentina and was quarantined in Sydney before travelling to Adelaide, where he tested positive.
Tougher mask rules as SA comes out of lockdown afr.com - get the latest breaking news, showbiz & celebrity photos, sport news & rumours, viral videos and top stories from afr.com Daily Mail and Mail on Sunday newspapers.
Mark Ludlow
Need to Know blog. Here’s the highlights from today.
NSW reported 145 new locally acquired coronavirus cases.
Fifty-one cases were in the community for their full infectious period, while a further 25 cases were in the community for part of their infectious period.
NSW Premier Gladys Berejiklian said she will announce changes to lockdown restrictions in coming days, and flagged that some rules could tighten.
Federal Labor has ended a six-year pursuit of policies aimed at curbing negative gearing and capital gains tax deductions for investors, as it seeks to minimise avenues of attack ahead of the next election.
COVID vaccine: Pfizer attempts to create malaria vaccine afr.com - get the latest breaking news, showbiz & celebrity photos, sport news & rumours, viral videos and top stories from afr.com Daily Mail and Mail on Sunday newspapers.
South Australia has recorded just one new case of coronavirus in the last 24 hours, from 23,410 carried out across the state.
Premier Steven Marshall said low case numbers meant the state was on track to come out of lockdown on Tuesday as planned.
However despite this positive news, Mr Marshall said all international flights into SA had been cancelled for two days next week. I can report to you that I wrote to the Prime Minister yesterday asking if we could cancel some international flights to South Australia, he said.
South Australian Premier Steven Marshall at this morning s update. (Nine) We have been very concerned with the very high numbers of testing that we will run out of capacity.