Silvercrest said all production at the plant will cease and this week's products will not be released from the plant.
It follows tests carried out by the Republic's Agriculture Department to try and establish the source of the contaminated material.
A statement from Silvercrest said: "Following receipt of this evening's Irish Department of Agriculture results, we believe that we have established the source of the contaminated material to one of these suppliers.
"However, because equine DNA has been found in finished products tested this week, we have decided that the responsible course of action is to suspend all production at the Silvercrest plant in County Monaghan with immediate effect.
"This week's production has not been released from the plant."
The company said all staff will continue to be paid during the suspension of production.
Earlier this week it emerged that scientific tests carried out by the Food Safety Authority of Ireland (FSAI) found traces of horse DNA in frozen burgers on sale in some of the UK and Ireland's leading supermarkets.
The survey uncovered low levels of the DNA in most products, which were sold in Tesco, Lidl, Aldi, Iceland and Dunnes Stores.
ABP Food Group pledged to introduce a new testing regime in the wake of the scandal.