The Road Safety Authority (RSA) is asking road users to prepare for hazardous conditions on roads and footpaths from Monday.
Met Éireann has issued a weather advisory for wintry hazards including frost and ice and the potential for sleet, snow, and hail throughout the week.
After the recent prolonged spell of mild weather, road users are being advised not to get caught out by a drop in temperatures.
The RSA said drivers should expect hazardous conditions with a potential for reduced visibility. Road users are also urged to exercise caution particularly on untreated road surfaces.
On Monday evening, snowfall accumulations are possible in Cavan, Donegal, Leitrim and Monaghan from 7pm to 8am Tuesday morning.
The RSA has warned that this could lead to poor visibility and difficult travelling conditions.
There is a low temperature/ice warning for Ireland from 8pm Tuesday to 10am Wednesday and 8pm Wednesday to 10am Thursday where it will be very cold with widespread frost and icy stretches.
This could lead to hazardous conditions on roads and paths and some travel disruption.
Road users are being advised to check local traffic and weather conditions before setting out on any journeys.