The Republic of Ireland's counterpart office, Met Eireann, issued a red wind warning across the country.
The hurricane will have weakened into a storm when it hits the UK on Monday, 30 years after the Great Storm of 1987.
Ophelia is on its way from the Azores in the Atlantic Ocean.
Northern Ireland's Department of Education said the decision on school closures was "entirely precautionary".
All schools and colleges in the Republic of Ireland, where "violent and destructive gusts" are forecast, will also be shut.
The Department of Education and Skills said the decision had been made "following discussions with members of the Government Task Force on Emergency Planning and in light of the advice from Met Eireann on this unprecedented storm."
Ireland's Taoiseach Leo Varadkar said defence forces were being sent to red weather alert areas - including Wexford, Galway, Mayo, Clare, Cork, Kerry, Limerick and Waterford.
More about: #hurricane #UK
