Cranswick Country Foods in Cullybackey is set to close temporarily from Saturday evening to allow all staff members to be tested for Covid-19, the company has confirmed.
Mr Swann told a press conference at Stormont that at least 35 cases have been identified.
He added: “All the workers and recent visitors to the factory should be required to self-isolate.”
In a statement Cranswick Country Foods said: “There has been a recent increase in the number of confirmed Covid-19 cases in Ballymena and the wider region and this has been acknowledged as a community issue.
“As a result of this, we can confirm that a number of colleagues at our Ballymena site have tested positive for Covid-19.
“Working with the Public Health Authority (PHA), we have taken the decision to send all of our colleagues for testing.
“If the test results are positive, the individual will be required to self-isolate for 10 days; if the test results are negative, the individual will be required to self-isolate for 14 days.
“Therefore, the site will need to temporarily suspend production.”
Meanwhile a nightclub in Belfast has announced it will not open after a staff member tested positive for Covid-19.
In a social media post, Thompsons said all other staff members have been tested and are awaiting their results.
“Sadly we cannot open until we are certain that everyone employed at Thompsons is in the clear,” they said.
“In the interim the entire venue is undergoing a deep clean, fumigation and decontamination in preparation for re-opening this weekend.”
New restrictions
It comes as another 51 people in the region have tested positive for coronavirus, according to the Northern Ireland Department of Health. Some 298 people have tested positive for the virus in the last seven days, bringing the total in the North to 6,556.
No further deaths with Covid-19 have been reported.
Mr Swann also told the conference that the "R" number in Northern Ireland is now 1.3, and announced a series of new restrictions.
The number of people allowed to meet indoors at households is to be reduced to six from no more than two households.
The limit on numbers at outdoor gatherings will fall from 30 to 15.
Mr Swann said there would be focused PSNI enforcement in hotspot areas.
Mr Swann added: “Unless we take action now I fear it would soon have been too late to arrest further extensive spread of the virus.”
Chief medical officer Dr Michael McBride backed the Stormont Executive’s decisions.
“I believe they send a signal to the community as a whole.
“They reflect all our concerns at the growing numbers of Covid-19 cases.”
Dr McBride said the reopening of schools was a priority and real harm was being caused to young people’s health.
He said there was a significant increase in the number of cases among younger people, adding that partly explained why a similar increase in hospitalisations had not yet been seen.
The medic said some of the evidence about people’s behaviour was anecdotal.
“We are seeing increased social mixing, close contact occurring in domestic settings.
“What we now need to do is act on that evidence and act on it in a proportionate way.”