Workers were informed of the decision on Thursday afternoon, as reported in The Irish Times.
The department stores, which are both owned by the Selfridges Group, employ of 1,000 people, not including concessions.
Brown Thomas has six stores, located in Dublin, Cork, Galway and Limerick, while Arnotts has one store on Henry Street in Dublin city centre.
The company hopes that a number of the redundancies will be made on a voluntary basis, with the consultation process beginning immediately.
Managing director of Brown Thomas Arnotts, Donald McDonald said the decision was needed to ensure the survival of the business.
“The retail industry is being severely impacted by unprecedented circumstances related to Covid-19 and Brown Thomas Arnotts is no exception. Like many others, we are feeling the effects with sales expected to be significantly down, making 2020 the toughest year we have experienced in recent times.
“And as we face continued uncertainty, with retail unlikely to return to normal for the foreseeable future, it is clear that we need to take a series of steps to ensure our cost base is sustainable, consistent with the level of business we realistically expect, and to ensure our resources are aligned with the current and anticipated requirements of the business.”