Pork processor Tulip Ltd has confirmed that a number of staff at its Midlands meat site have tested positive for Covid-19.
Ten staff from a workforce of about 640 in Tipton, West Midlands, had tested positive for the virus.
The firm said: "We are working with Public Health England to arrange swab testing for a sample group in one particular area of production before deciding upon the need for any further screening.
"As soon as we receive test results, we will liaise with health partners to assess whether further actions are necessary."
The processor has also confirmed that the Tipton plant will close, following a consultation with employee representatives that began in March.
Public Health England Midlands is now working with Sandwell Council, the Health and Safety Executive (HSE) and the NHS to support the pork firm.
A joint statement said: "In line with NHS guidance, any affected individuals are being asked to self-isolate at home for seven days, with members of their households to isolate for 14 days.
"Public Health partners are working closely with management to assess actions to be taken and any further measures needed to ensure working practices are as safe as possible."
PHE has stressed that the risk of contracting the coronavirus through the UK food chain is very low.
“There is currently no evidence to suggest transmission occurs through the foodborne route, therefore people are very unlikely to catch Covid-19 from food,” a spokesperson said.
A number of UK meat plants have been affected by the pandemic, including 2 Sisters's Anglesey chicken site where more than 200 people have tested positive.