NHS Ayrshire and Arran's COVID-19 Test and Protect team has told several staff members at Tesco in Saltcoats to self-isolate.
The workers are being told to self-isolate at home for 10 days after coming into contact with a positive case of coronavirus.
Joy Tomlinson, Joint Director of Public Health at NHS Ayrshire and Arran, said: "The workplace has physical distancing and hygiene processes in place to minimise the risk of viral spread and to support Test and Protect. The risk to the public is considered low.
"All relevant Public Health measures are in place and our Public Health Team is working with North Ayrshire Environmental Health Officers to manage and monitor the situation.
"To respect and maintain patient confidentiality it is not possible to release any further information at this time."
Ms Tomlinson said it was a "small number of individuals" that are being contacted by the Test and Protect team.
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