The first and deputy first minister have offered their sympathies to the family of Luciana Viviana da Silva, a worker at Moy Park's Dungannon processing plant who died after contracting Covid-19.
Arlene Foster said in the Assembly that she was "shocked" to hear of the death of 58-year-old Ms da Silva, who was from East Timor.
"We do send our sympathy to the family of Ms da Silva. I was very shocked to hear that it had happened in Dungannon and that she had lost her life in that way."
Deputy First Minister Michelle O'Neill said there would be a full investigation into the circumstances surrounding Ms da Silva's death.
"Obviously there will have to be a full investigation into what happened in her own circumstance and I would encourage that between both the employer and the HSE. But I would say very clearly to all workers out there that nobody should be working in unsafe practice," she said, speaking on Tuesday.
Meanwhile, a spokesperson for Moy Park said earlier on Tuesday that the poultry giant had worked with the Public Health Agency, DAERA and the Health and Safety Executive to adhere to their coronavirus advice and protocols.
Speaking in the Assembly, Sinn Fein MLA Colm Gildernew raised concerns about the Executive's ability to reach certain members of the community with information on the virus.
"I was very saddened today to hear of the death of a foreign national worker in Dungannon, some of our most valuable workers," he said.
"We know from testing in the south of Ireland that there are particular clusters emerging in the food processing sectors, largely due to the fact that the people working are living in multiple occupancy housing, they have language issues."
Earlier on Tuesday, poultry giant Moy Park said the health and wellbeing of their workforce is their most important consideration as they sent condolences to the family of Ms da Silva.
They issued the statement after Unite the Union wrote to the first and deputy first ministers on Monday to demand testing for workers in the poultry and meatpacking sector.
The union said urgent action is needed by Stormont after reports of clusters of infection at a growing number of sites.
It said Moy Park's plant in Dungannon, Co Tyrone, should be shut down to allow the workforce and their families to be tested if necessary - and for the Health and Safety Executive (HSENI) to conduct physical inspections of meat processing sites to assess infection controls.
A spokesperson for Moy Park said: "We are deeply saddened to learn of the death of one of our team members. Our thoughts are with Luciana’s family and friends at this incredibly difficult time.
"As we have consistently stated, the health, wellbeing and safety of our Moy Park team members is always our most important consideration. It is all the more disappointing therefore to have to respond to these inaccurate claims made by Unite the Union."
Unite has been approached for a comment.
The spokesperson said Moy Park worked quickly with all key parties, including government and industry bodies as well as workers and unions as the coronavirus crisis unfolded.
They said the firm implemented bespoke solutions which are now considered to have led the way for food processors, including installation of perspex screens, social distancing on their various sites, enhanced cleaning and incentive payments to site-based team members.
The firm is also introducing thermal temperature scanning for all team members as they arrive at work, the spokesperson said.
"These measures have been in place for some time at all our sites and are stringently followed. These are also exactly the type of measures that government guidance is now calling for as other industries return to work.
We continue to consult, evolve and review our measures to ensure rigorous safety," they said.
"We reiterate, Moy Park follows all government guidelines and works closely with the Public Health Agency, DAERA and the Health and Safety Executive, adhering strictly to their advice and protocols.
"We have received positive feedback following a recent unannounced inspection by the HSE that was conducted at one of our other sites, which has the same measures in place to those at Dungannon.
"The inspection focused solely on the controls which we have in place to ensure employee safety in relation to COVID-19. We will continue to update our procedures in line with their guidance."
On Monday, Unite said it was aware of a number of cases among workers at Linden Foods in Dungannon, as well as the death of Ms da Silva.
Regional Secretary at Unite Jackie Pollock said: "We need to see immediate action in light of this news and the emerging Covid-19 clusters which are emerging at poultry and meatpacking sites.”
Mr Pollock said Unite is concerned that workers are still contracting the virus. He claimed current guidance and enforcement measures are not going far enough to protect their health and safety.
On Monday, a HSENI spokesperson said discussions are currently ongoing with Moy Park to understand the circumstances around Ms da Silva's death.
"We can confirm that a recent unannounced inspection was carried out at a Moy Park meat processing plant. A few minor issues were found but the overall compliance with the PHA COVID-19 guidance was found to be of a high standard. This approach will continue."