Cranswick at Cullybackey, which processes pigs, will close for a complete cleaning and body testing of workers.
Health Minister Robin Swann said 35 cases had been known at the plant, which has 500 workers.
The company reported its on Thursday, and the closure will take effect on Saturday at 18:00 BST.
A group is like two or more cases.
A corporate spokesman said staff welfare is the main concern.
“There has been a recent increase in the number of cases shown of Covid-19 in Ballymena and in the region as a whole and this has been identified as a network problem.
“As a result, we can verify that several colleagues in our Ballymena have tested positive for Covid-19.
“In collaboration with the Public Health Authority (PHA), we have taken the resolution to send all our colleagues to look. If the effects are positive, the individual will have to isolate himself for 10 days; if the effects are negative, the user will have to isolate himself for 14 days.
“As a result, you will have to temporarily suspend production.”
The Public Health Agency said it had made a “series of recommendations” to a company in the Middle Council region and is from Antrim.
“These come with evidence throughout this week and self-isolation of cases known as close contacts.”
He said tests and studies were being conducted to identify who could potentially be assigned to help him save a new network transmission.
He said he would not comment on individual cases to prevent other people with the disease from being known or to discourage others from making the most known.
There has been a recent increase in network instances in the Antrim Middle and East Council domain with 80 new instances in the following seven days.
Cranswick will be the first meat company to close The Covid pandemic in Northern Ireland, but not the first to have cases among its workforce.
Several of them have closed their doors in the Republic of Ireland and Europe in recent months as a result of Covid clusters.
Conditions in meat plants are thought to be for disease transmission.
Cool temperatures and other people running nearby on noisy production lines can make this easier.
The fact that some meat plant staff members have a tendency to live or in combination could also be a factor.
But processors have spent a lot of cash to put in place measures to verify and mitigate the risk.
These come with non-public protective devices for workers, screens to separate workstations on production lines and staggered schedules.
There were protests in Northern Ireland meat mills at the start of the pandemic, as they complained about some companies that responded to their protection concerns.
This has resulted in new instructions for food processors.
The Health and Safety Executive said he carried out inspections at meat processing plants in Northern Ireland between 28 April and 17 August.
Cranswick processed more than 10,000 pigs a week at his Ballymena plant.
It is understood that they are negotiating with other corporations to take those animals whose scenario is resolved.