It is understood employees at Tara Mines have ceased working, after talks at the Workplace Relations Commission ended without agreement on Wednesday.
The talks centered on the company's plan to temporarily suspend the Co Meath operation and lay off 650 workers next week.
Its owner, Boliden Group, said this was due to a combination of factors - including rising energy bills and a drop in the price of zinc.
The move comes as the Irish Congress of Trade Unions will debate an emergency motion calling for an immediate and major intervention by the Government to protect the future of Tara Mines at its Biennial Delegate Conference.
SIPTU Division Organiser Adrian Kane said workers were angry at the lack of progress at the talks.
"I think that that sense of anger, in terms of how the issue has been managed by management to date, has boiled over," he said.
"I understand that work has come to a stop on the site.
"We were at the Workplace Relations Commission yesterday, and very little progress was made," he added.
On Tuesday, SIPTU Sector Organiser John Regan said the situation was completely unacceptable.
"Boliden, the owners of Tara Mines, has yet to present to unions with a satisfactory outline of what it envisages providing its employees in terms of a retainer and other payments in the event of a lay off," he said.
"This is a completely unacceptable situation and does not bode well in terms of where this dispute is heading," he added.
Tara is Europe's largest zinc mine, and the eighth-largest in the world.
More than 85 million tonnes of ore have been extracted there since mining began in 1977.
Stockholm-based Boliden Group acquired the mine back in 2004.