Met Éireann has issued a status yellow snow-ice warning for Connacht, Cavan, Monaghan, Donegal, Longford and Louth.
The forecaster said falls of hail and sleet and snow are expected, with accumulations mainly affecting higher ground.
It said snow could also affect lower areas.
Met Éireann said there will also be a risk of icy patches resulting from the falls hail, snow and sleet.
Some of the wintry showers may spread to other areas towards dawn.
Temperatures are expected fall to between -1 and +3C overnight resulting in widespread sharp frost.
The warning will take effect from midnight and remain in place until midday on Wednesday.