Road conditions will deteriorate.
Met Éireann has issued a Status Yellow snow and ice warning which will affect 22 counties.
The warning is in place for Munster, Leinster, Cavan, Monaghan, Galway and Roscommon.
It was issued at 10am on Sunday and is valid from 2pm on Sunday until 8am on Monday.
The meteorological service said that heavy rain will turn to sleet and snow on Sunday.
But they did say that much of the snow will be above 300 metres with just a local dusting of snow at lower levels.
Motorists were also advised that wet and slushy roads will likely become icy in places overnight as temperatures drop below freezing, creating dangerous road conditions.
The last of the rain, sleet and snow will clear into the Irish Sea on overnight with strong northwesterly winds developing near the south coast and over parts of Leinster for a time.
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