Coles in Westfield Hurstville is among a large number of venues included in a COVID-19 alert, issued on Sunday evening.
NSW Health says anyone who attended the supermarket on Saturday June 19 from 6.10pm - 6.30pm is classified as a casual contact and must immediately get tested and self-isolate until a negative result is received.
"Please continue to monitor for symptoms and immediately get tested and isolate if they develop," a statement said.
The other locations included in the alert are in Drummoyne, Castle Hill, Merrylands, Sydney CBD, Parramatta, Castle Hill and Baulkham Hills.
NSW Health has not yet issued an alert for any venue in Sutherland Shire. Two COVID cases in the shire were announced earlier on Sunday.
NSW Health said people who do not have symptoms and have not been at the specific exposure venues at the listed times do not need to isolate.
However, they strongly urge everyone to avoid gatherings and minimise their movements, such as not attending the cinemas or trips to the ski fields.
"If you can work from home, please do so," NSW Health says.
Masks are now mandatory on public transport in Greater Sydney and the Blue Mountains, and the Wollongong and Shellharbour local government areas. In addition, masks are now mandatory in all public indoor venues in the City of Sydney, Waverley, Randwick, Canada Bay, Inner West, Bayside, and Woollahra local government areas.
These venues include retail, theatres, aged care facilities and masks are also mandatory for front-of-house hospitality staff.
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