Hays Travel, which has around 20 branches in Northern Ireland, is to cut up to 878 jobs out of a total workforce of 4,500 people, the firm announced.
The travel company said it has "made every possible effort" to avoid job losses "during these extraordinary and distressing times".
Around 1,700 jobs UK-wide are also at risk at sports retailer DW Sports after it went into administration. There was no information on how many Hays Travel jobs would be affected in Northern Ireland. It acquired around 500 UK travel agent shops from Thomas Cook when it closed last year.
It was "on track for recovery" when the Foreign and Commonwealth Office stopped advising against all non-essential travel in early July, but the recent decision to reintroduce restrictions for people going to Spain "triggered the cancellation of hundreds of thousands of holidays".
Owners John and Irene Hays said: "We are devastated that after all of our efforts and the huge investment we've made, we now face losing some of our valued employees, through no fault of their own.
"Following the decision to ban travel to Spain and the changes in furlough conditions coming at the same time, we have had no choice. We are also devastated for everyone who may lose their job and we will do all we can in consultations to help them, as we focus on retaining as many people as possible."