A supermarket and a McDonald's restaurant near Adelaide Airport have been cleared to keep trading after coronavirus cases were discovered among their staff.

Key points: The supermarket staff member worked at the store on Monday and Tuesday this week

The supermarket staff member worked at the store on Monday and Tuesday this week McDonald's Australia has also confirmed a positive case at its Fulham Gardens store

McDonald's Australia has also confirmed a positive case at its Fulham Gardens store SA Health has cleared both outlets to continue trading

The cases are believed to be linked to a cluster at the airport.

SA Health announced 11 new COVID–19 diagnoses today, bringing the state's total to 396, including 19 connected with Adelaide Airport Qantas baggage handlers.

Both McDonald's and the Drakes Supermarket at Fulham Gardens are in close proximity to a National Pharmacies store at Findon that was yesterday closed due to a positive case of COVID-19.

The nearby Henley High School was also closed yesterday after confirmation that a student had tested positive.

Drakes Supermarkets said one of its female staff members who had worked at the store, in Adelaide's west, had tested positive to COVID-19.

John-Paul Drake told the ABC that 18 staff members were now self-isolating as a precaution.

"She is actually asymptomatic, so she has no symptoms at all," he said.

Eighteen staff members from the Drakes Supermarkets store are self-isolating. ( ABC News: Michael Clements )

"The team member got home and found out her parents had COVID-19 on Tuesday, she was then tested and then she got her results back on Thursday afternoon.

"She hadn't been in to work at all since her last shift which was on Tuesday ... she didn't come back into the store while she was waiting for a result."

A letter has also been posted online by the head of Drakes Supermarkets, Roger Drake, who said the customer service team member had worked in the store on Monday and Tuesday.

He said he believed the case was linked to a cluster of infections among Qantas baggage handlers at Adelaide Airport.

He said the store had been given the all clear by SA Health to remain open as "the risk of transmission for customers and team members has been deemed extremely low".

"The team member is in isolation and we will continue to work with this team member to ensure their health and wellbeing moving forward," Mr Drake said in the letter.

"We continue to take all necessary precautions to protect our team, and all who enter our store."

He said the store would receive thorough sanitisation and all staff members who were in direct contact with the team member had been advised to self-isolate.

Contact tracing is currently being undertaken and anyone who visited the store between Monday and Wednesday this week and becomes unwell has been asked to seek testing.

McDonald's staff member tests positive

A crew member from a McDonald's restaurant at Fulham Gardens has also been confirmed as a positive case of COVID-19, with the worker currently self-isolating.

The crew member worked at a McDonalds restaurant in Fulham Gardens. ( ABC News: Michael Clements )

In a statement from McDonald's Australia, a spokesperson said SA Health had advised that the restaurant could continue to trade.

"There is no suggestion the crew member was exposed to COVID-19 in the restaurant," a spokesperson said.

"The health and safety of our people and our customers is our priority and upon receiving notification of the diagnosis from the South Australian Department of Health, we immediately commenced notifying all employees.

"McDonald's Australia uses high-grade cleaning products throughout the strict cleaning, quality control and hygiene procedures that are adhered to in every shift at each of our restaurants."

Two subcontractors working on the redevelopment of Her Majesty's Theatre in Adelaide's CBD being undertaken by Hansen Yuncken have also tested positive for the virus.

One worker at the construction site who had close contact with the workers has gone into self-isolation.

Project director Scott Brumfield said a "deep clean of the affected areas" had been done.

Thousands cross border after restrictions

Police Commissioner Grant Stevens said 9,500 people had come across the state's borders since restrictions came in last week.

He said about half were required to go into self-quarantine, while the other half had been deemed essential travellers or people living near borders.

He said there were no plans to restrict travel to Kangaroo Island, which recorded its first positive case yesterday.

Premier Steven Marshall said he was pleased with the number of cases being diagnosed each day.

"We are moving into a phase now where the numbers are not moving in an exponential growth rate like we are seeing in some other parts of the world," he said.

A shop in Rundle Mall which chose to close because of coronavirus. ( ABC News: Dean Faulkner )

Pennington R-7 School and Pennington Children's Centre, in Adelaide's western suburbs, were also closed yesterday after positive coronavirus cases.

In a letter to parents on Wednesday, principal Georgina Grinsted said the school and kindergarten "will not be opening again until public health officials indicate that it is safe to do so".

SA Health will conduct contact tracing to determine which staff or students should go into quarantine.