The company said a small number of its workers at the Ocotal Way Extra store had been infected with the virus in recent days and those who tested positive were self-isolating at home.
No delivery person was infected and the store remains open.
“The safety of our customers and colleagues is our top priority,” said a spokesperson for Tesco.
“We have extensive measures in place at all of our stores to help keep everyone safe, including protective screens at each checkout, social signage and regular deep cleaning.
The outbreak comes days after around 51 workers at an Icelandic warehouse tested positive for COVID-19[feminine[feminine in Swindon.
Health chiefs said mobile screening teams had been called after the cluster of cases and many of the new cases detected were asymptomatic.
Swindon City Council for Adults and Health cabinet member Brian Ford said the recent coronavirus case was prompted by the outbreak at the Icelandic food distribution center.
Three crew members from the Swindon fire station were also diagnosed with the disease, while local Honda and Royal Mail depots suffered from ‘small outbreaks’ following the easing of lockdown restrictions .
The map below shows Swindon’s seven-day case rate is among the highest in the UK, at 47.3 per 100,000 people.
Steve Maddern, director of public health for Swindon, said: “Small outbreaks are expected as the lockdown arrangements are eased and people return to work.
“We have developed a local outbreak management plan to complement and support the national test and traceability service, and to ensure that Swindon can respond quickly to help manage an outbreak or a local hotspot.
“The council is currently responding to a small number of COVID-19 cases, and these people are self-isolating under government self-isolation guidelines. ”
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Mike Wade, health protection consultant at Public Health England South West, said “everyone should follow social distancing advice, both at work and outside of work” to prevent the spread of COVID-19 .
“Good hygiene is the best prevention and there are some simple steps you can take to protect yourself, your family and colleagues by washing your hands regularly and thoroughly and if you cough, cover your mouth and nose with it. a handkerchief, ”he added.