The supermarket giant has owned Kober Ltd since 2016, and the plant supplies Asda with bacon products.
A 'small number' of cases have been identified and the government's new track and trace system has been deployed to find people the affected workers have been in contact with.
The factory has now been shut down, with staff in self-isolation receiving full pay.
A statement from Asda and Kober Ltd read: “As soon as we became aware that some colleagues at our Kober site may have Covid-19, we responded swiftly and worked collaboratively with the local authority and Public Health England to test all colleagues. We have also voluntarily closed the site to protect colleagues and prevent any further transmission. Colleagues who need to self-isolate will receive full pay and we aim to reopen the facility early next week. We’re grateful to the Kirklees Council and Public Health England for their support through this process.”
Mobile testing tents have been set up outside the factory - the second meat processing plant in Yorkshire to suffer a Covid-19 outbreak after three workers at Cranswick Convenience Foods in Barnsley died in May.