Deputy First Minister Michelle O'Neill has said historic manufacturer Ulster Carpets should close to protect employees during the coronavirus outbreak.
And she said she would use "every legal power" to shut other premises where non-essential work was being carried out.
Ulster Carpets is continuing to operate its Portadown factory, where around 600 staff are employed.
Certain types of businesses such as shops selling non-essential goods have been ordered to close.
But factories can stay open, provided proper social distancing measures are observed and staff are allowed to work from home where feasible.
Ms O'Neill said the carpet maker is "absolutely not" carrying out essential work and "should be shut down". She said non-essential businesses who are telling their staff to come to work should be ashamed and need to "give themselves a shake".
She said the authorities such as the Health and Safety Executive would not hesitate to take enforcement action against offenders.
The Deputy First Minister added: "I would say to anybody who works to get government contracts, I don't think anybody should look kindly on people who don't do the right thing in this period, and that includes what we do in government... I think that everybody should ask themselves this question. When you look back in this period in our history, did you do the right thing?
"Employers should really give themselves a shake, if they're not doing the right thing.
"I would use every bit of legal power available to me to shut people down who are doing the wrong thing."
Ulster Carpets did not wish to comment but defended its measures to enforce social distancing at work. A caller to Radio Ulster's The Nolan Show claimed the company was not observing correct social distancing policy during "highly populated" shifts.
But a company spokesman said: "The company is fully following government guidelines, has enacted working from home for all employees who can, has introduced measures to support two-metre distancing in our facilities, is encouraging and enabling frequent hand washing, and has ensured enhanced cleaning is taking place on a frequent basis."
Meanwhile, workers at Irish insulation products company Kingspan, which employs 400 people in Portadown, has asked its staff on the island of Ireland to accept a 40% pay cut. However, a separate staff retention scheme in the UK would refund firms with 80% of staff wages.
Chief executive Gene Murtagh and other senior staff are to accept a 50% pay cut. A spokesman said: "We are examining the UK Government scheme to support the pay of staff impacted by coronavirus, and where possible we will look to see if this can be applied to deliver the best financial outcome for our employees.
"In no circumstances will any employee have their pay reduced to a level to take them below the hourly minimum wage."