There is a "possibility of snow" on mountain tops on Tuesday night as the east is set to be lashed by heavy rain.
Met Eireann is forecasting outbreaks of rain, which will turn heavy at times, in the east and southeast.
And the downpours may lead to snowfall on top of the Wicklow Mountains.
A forecaster said: "Tuesday night will see outbreaks of rain in the east and southeast will turn heavy at times with the possibility of snow on the tops of the Wicklow Mountains.
"There'll be showers in the southwest and south with the rest of the country seeing drier conditions.
"Temperatures will fall to between plus 1 and plus 3 degrees with light to moderate southeast to east winds, temperatures will be a little higher in the southwest."
Earlier on Tuesday will be mostly dry and sunny, before rain moves over the country in the evening.
Highest temperatures will range from 7C to 11C in the afternoon.
A forecaster said: "Tomorrow outbreaks of rain will move eastwards over the country, arriving in the east in the early evening, while mainly dry and sunny weather follows into the west.
"Highest temperatures of between 7 and 11 degrees with moderate southeast winds, fresh in the north, and veering southerly for a time."
Although the temperatures later in the week will be "lower than usual for the time of year", Met Eirean is forecasting "frost free" nights.
