Tulip has had around a dozen staff at its site in George Henry Road Road test positive for coronavirus.
The company has also confirmed it has reached a decision to close down its fresh pork manufacturing site following a collective consultation process with employee and union representatives.
This was communicated to all employees upon the end of consultation last Wednesday.
Tulip had announced in March that it was looking at closing the site where 600 people work.
"The business is now in individual consultations with those impacted by this decision," the company, which has its headquarters in Warwick, said.
"Support is being made available to all those implicated in the site closure to explore opportunities for redeployment within the Tulip network as well as employment opportunities outside of the business in the local area.
A joint statement on the Covid-19 cases was also issued by Tulip, health organisations and the local authority, which said: "Public Health England Midlands is working with Sandwell Council, the HSE and local NHS colleagues, to support meat processing business Tulip Ltd, following confirmation of some cases of Covid-19 in staff members.
"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.
Dr James Chipwete, PHE Midlands consultant in communicable disease control said: “The management at Tulip Ltd are cooperating fully with public health professionals and members of the HSE, to protect the health and wellbeing of their workforce.
“We are dealing with a large workforce of almost 600 people, and despite putting a range of infection control measures in place to protect staff from potential exposure to Covid-19, there have been a number of cases among workers. W
"e are therefore liaising with management, the local authority and the Health and Safety Executive to advise on increased social distancing measures. We are also working with local NHS colleagues to arrange testing for a group of the workforce that have seen the most cases of Covid-19 over the last month.”
A spokesperson from Tulip said: "Safety is a condition within our business. When restrictions were introduced, and government guidelines issued in relation to coronavirus and food processing sites, our business has been working to these guidelines and liaising with UK Government, the Food Standards Agency, the Health and Safety Executive and Public Health England on all matters including social distancing and its application in food processing factories.
“We are proud of our team members at Tipton who, as key workers, have bravely responded to this global pandemic in the most challenging of local circumstances; their health and wellbeing is of the utmost importance and we welcome PHE Midlands’ support during these unprecedented times.
“We are working with PHE Midlands 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.”
An employee at Tulip, Tipton, who did not wish to be identified, said: "At present there have been around 12 to15 reported positive Covid cases."
He added: "We are all worried about our safety there but no one seems to be concerned about the ever increasing positive cases."