Met Éireann has issued a status yellow warning for low temperatures and ice which will come into effect this evening.
The forecasters say there will be hazardous conditions on roads and paths overnight due to freezing temperatures.
Lowest temperatures are likely to fall to between 0 and -4 degrees leading to widespread sharp frost.
Wintry showers will later move into north facing coasts later, in mostly light northerly breezes.
The warning will begin at 6pm today (Monday) and remain in place overnight until 10am on Tuesday.
All counties in the Republic are affected by the warning.
Tuesday will remain very cold but there will be plenty of sunshine too across the West.