Melbourne shoppers have been put on high alert after employees tested positive to coronavirus at a Coles supermarket and a Kmart store in the city's south-east.

Kmart Chadstone is the latest store to have confirmed cases of COVID-19, with two casual staff members testing positive to the virus.

Chadstone management will now make contact with every retailer at the centre but said the area outside Kmart has been throughly cleaned.

A notice, obtained by 9News, stated the Kmart store had been closed due to a confirmed case of COVID-19 .

Chadstone remains open from 10am to 5pm.

A Kmart store has closed in Melbourne due to a confirmed case of COVID-19. (Supplied Nine)

"Our store is currently closed for cleaning following a confirmed case of COVID-19," it read.

"Our priority is to ensure the safety of our customers and team members. We apologise for any inconvenience."

9News understands staff were alerted to the cases of infection via text message today.

A Kmart spokeswoman confirmed the team members last worked on Saturday.

"We can confirm that today two casual team members at the Chadstone store who worked on Saturday 28 March have returned a positive result for COVID-19," she said.

"As soon as we were made aware, we immediately closed the store as a safety precaution and commenced a thorough sanitisation of the store.

"We are working closely with the department of health and have been advised that there is minimal risk to any customers."

COVID-19 cases in Coles and Kmart. (Nine)

Two staff members at Coles Brandon Park store in Mulgrave have also tested positive to the virus, with one employee working at the adjoining Liquorland store.

The team members did not work together and have self-isolated at home.

Coles in a statement to 9News said the store would remain open despite the positive test results.

"Coles has conducted a full clean of the stores over and above the recommendations from the Victorian Department of Health and Human Services (Department of Health), which has confirmed that the stores can continue to trade and the risk of transmission for customers and team members is very low," the statement read.

"In addition to criteria on hygiene and social distancing practices, the guidelines specify that 'there is no requirement to close a store if a staff member tests positive for COVID-19.'"

Team members who have come into close contact with the pair have also been instructed to self-isolate and seek medical treatment should they display symptoms.

Two staff members at a Coles in Melbourne's south-east have tested positive to COVID-19. (AAP)

Melbourne construction site shuts down after worker tests positive

A worker from a Melbourne inner-city construction site has tested positive to COVID-19.

The employee, who was working at the Multiplex Melbourne Square site on Kavanagh Street in Southbank, returned a positive diagnosis at 6pm last night.

"Multiplex was notified last night that a worker who attended work at our Melbourne Square site was found to have tested positive for COVID-19," Regional Managing Director Multiplex Graham Cottam said.

"We immediately carried out a full clean and sanitisation of the site in accordance with latest protocols. Upon appropriate clearance we anticipate work recommencing within 24 hours.

"Those working in close contact with the affected worker have been asked to self-isolate in accordance with Department of Health recommendations.

"Health and safety is of paramount importance to us and we are taking every necessary precaution for the wellbeing of our people and the broader community."

The worker began displaying symptoms after his partner was diagnosed with COVID-19.

His partner became unwell the week prior.

The CFMEU confirmed the worker immediately self-isolated after his partner's positive test result.