Food production at the processing facility in Holton, near Halesworth in Suffolk, has not been affected by the outbreak.
Around 100 staff have been tested for Covid-19 with most returning negative results and additional testing is taking place this week.
The site has had controls in place since March to reduce coronavirus infections.
This includes regular temperature checks, staff working in bubbles, Covid marshals, masks and visors and social distancing throughout the site.
The majority of the 18 workers who tested positive live in the Great Yarmouth and Lowestoft areas and the cases are believed to have initiated in the community, the company said.
Officials including from Suffolk County Council, Public Health England and Bernard Matthews are working together to manage the situation.
Stuart Keeble, Suffolk’s director of public health, said: “I’d like to reassure people that this is, at this stage, a relatively small number of cases and that the situation is being very carefully managed by all the partners working closely together.”
A spokesperson for Bernard Matthews said: “We are grateful for the help of all local agencies and we fully support their objectives to protect the local community.
“We believe these small number of cases were initiated in the community, but nevertheless we will continue to enforce our robust Covid measures as we enter into our busiest period of the year.”
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