Julia Burrows, director of Public Health, said an individual admitted ‘awaits the final laboratory results’.
To avoid catching or spreading the virus, the NHS has urged people to wash their hands with soap and water for at least 20 seconds or use hand sanitiser if soap and water are not available.
Ms Burrows wants to reassure people that the council are working closely with their health partners and arrangements are in place to manage the situation.
She said: “We’re awaiting confirmation about a presumed positive case of COVID-19 - coronavirus - in Barnsley.
“First, we send our best wishes to the individual and their family as they await the final laboratory results.
“I want to reassure people that anyone who has been in close contact with that individual will be contacted by Public Health England.
“I would also like to reassure people that we are working closely with our health partners and arrangements are in place to manage the situation.
“For the rest of our residents, it’s really important to emphasise that the risk is low, and they should continue to go about their daily lives as normal.”