Four members of staff have tested positive for the virus in Glanbia's Ballitore facility.
The company says business continuity processes have been escalated at the facility, and that the health and safety of employees, customers and suppliers is its top priority.
It comes as the Midlands regions of Kildare, Laois and Offaly remain under local lockdowns to halt the spread of Covid-19 following recent outbreaks of clusters linked to meat processing plants.
Kildare had the most Covid-19 cases of any county in the latest daily figures released, with 26 located in the county out of a total 56 new cases announced yesterday.
The Cabinet is meeting this afternoon to consider new restrictions following an emergency meeting of the National Public Health Emergency Team (NPHET) yesterday in response to a spike in Covid-19 cases over the weekend.
Indication on whether the local lockdown in Kildare, Laois and Offaly will be lifted on Sunday night as originally planned may also be expected.