Workers at Linden Foods in Dungannon have walked out over a "total absence of social distancing measures", Unite trade union has said.
They refused to start shifts and have asked for talks with management.
Linden Foods said its priority was ensuring the health, safety and wellbeing of its employees.
It comes as an updated list of businesses considered to be essential and allowed to open is due to be published.
Arlene Foster said businesses which could put social distancing in place could remain open.
She said the "essential businesses" list would be updated following the passage of the Coronavirus Bill through Parliament.
On Thursday night, Justice Minister Naomi Long said off licences were no longer deemed to be non-essential and could open if it was safe to do so.
Linden Foods said that approximately 40 employees had not attended work on Friday.
Unite regional officer Brian Hewitt said there was no social distancing at Linden Foods on the boning line, in the canteen, in changing areas or at entry and exit points.
He added that management had provided no additional wash facilities and failed to stagger breaks.
Mr Hewitt said: "Everyone needs to take responsibility but the company's actions are putting workers needlessly at further risk."
In response Linden Foods said it had been "actively implementing a range of measures across all our sites to provide a safe working environment".
These measures included increasing canteen size, erecting handwashing units and staggering breaks.
The statement added: "We fully appreciate and respect our teams who continue to attend work as key workers, ensuring that the food supply chain functions smoothly to keep the nation fed."
On Wednesday, staff at poultry firm Moy Park left their stations at its Portadown processing plant, claiming that social distancing was not being adhered to.
Moy Park said it has put new "robust" measures in place to protect staff, including staggered breaks and screens on some production lines.
Speaking on BBC's The View, Mrs Foster said: "We now have regulations to make in terms of essential and non-essential businesses, so we have to work through that.
"We also need to bear in mind that once we come out the other side of this terrible time we are going through - and which will be with us for some considerable time - we need to make sure we have an economic base to come back to.
"If you are operating a business and you can have safe working practices then you can continue to do that."
A list of businesses which could and could not open in Northern Ireland was published by the executive on Tuesday.
Off licences were not included among those allowed to open, unlike in the rest of the UK.
Some people had expressed concern, including SDLP assembly member Matthew O'Toole, who wrote to ministers about the issue.
He said responsible drinkers were entitled to have a drink "at a time when so many other liberties are being restricted" and also expressed concern about those with serious addictions "suddenly losing access to alcohol" which could lead to pressures on the health service. "
Mrs Long said they were no longer required to close, but were still not "essential" and it was down to individual owners to decide if it was safe to open.
Yes. Off licences are not listed as essential: however, they have been removed from the list of premises ordered to close.— Naomi Long MLA (@naomi_long) March 26, 2020
It is for individual off sales to judge and justify remaining open and to provide proper protection for their staff if they do.
Robin Swann thanked local businesses for coming forward.
It is planned that 20,000 ventilators will be manufactured and bought by NHS England and allocated across the UK.
Mr Swann said the firms had offered "their skills and expertise to assist the effort to provide those on the front line with the precious resources that they need".
The finance and economy ministers also praised the response.
They said 30 responses came from companies who will be involved in the UK-wide push to produce ventilators.
The ministers also said a cross-government PPE group has been established which will oversee orders with a view to expand the number of suppliers to government.
Help from businesses
Meanwhile, companies in Northern Ireland have offered to help supply critical items.
More than 100 companies responded to the government's call for help in sourcing critical items in the fight against Covid-19, the health minister said.
Ventilators, personal protective equipment (PPE) and hand sanitisers are among the required items.
He added that staff concerns over PPE were being treated "very seriously".
The director of the Royal College of Nursing (RCN), Pat Cullen, said nurses she had spoken to were "terrified" going into their work over the lack of appropriate PPE.
She said the effort needed to be "stepped up" and nurses were "really, really afraid every day and night".
"Nurses coming off night duty last night contacted me very concerned about this," she told BBC Good Morning Ulster.
"This is not finger pointing. Everyone is trying to do their best, but the bottom line is it's not available in the quantities and at the level that it is needed," she said.
"If you are afraid going into work every night because you do not have the PPE that you need - that's a very difficult place for nurses to be in," she added.
There have been 241 cases of coronavirus in Northern Ireland to date and 10 coronavirus related deaths.