Letterkenny and Sligo University Hospitals have deferred all non-urgent procedures and appointments until further notice.
Saolta Group, which operates both hospitals, says the decision was made to ensure they have the capacity to deal with any spike in Covid-19 cases.
The group is asking patients not to attend the hospitals unless they have confirmed their appointments are going ahead.
It comes as the INMO have announced that there are just 35 patients waiting for beds in hospitals nationwide.
The worst affected is St Vincent’s University Hospital in Dublin with nine patients on trolleys. University Hospital Kerry has five.
In University Hospital Limerick there is just one patient waiting for a bed, according to the INMO’s daily TrolleyWatch figures.
The mid-west hospital had a record 92 patients on trolleys on January 6.