Met Éireann has issued a nationwide status yellow ice and low temperature warning from 4pm on Monday to noon on Tuesday.
The national weather forecaster has warned of icy stretches that could lead to hazardous travelling conditions, especially on untreated roads and paths. Wintry showers in the northwest and southwest are expected.
Monday will remain cold with sunny spells. Scattered wintry showers will continue in parts of north Ulster and the far southwest. The icy conditions will clear slowly throughout the day, but may linger in places, Met Éireann said.
Temperatures will rise to just above freezing on Monday, at 1-4 degrees, with light northwest breezes.
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Temperatures are expected to drop to below freezing again overnight, with widespread severe frost, patches of mist and fog and icy stretches. Temperatures will hit lows of -1 to -5 degrees. Frequent wintry showers will develop in the southwest, Met Éireann said.
Showery outbreaks overnight of sleet and snow will affect parts of the north, northwest and southwest with some snowfall accumulations, especially on high ground, it said. It will be dry elsewhere with clear conditions.
Tuesday will remain cold with frost and ice in many areas. Scattered showers will be most frequent in Connacht and Ulster and later in the southwest. Isolated thunderstorms and fall of hail, sleet and snow are possible, especially in the evening, the forecaster said. Temperatures will reach 1-4 degrees.
UK Met Office has issued a status yellow snow and ice warning for Northern Ireland, which is in place from noon on Monday to Tuesday noon. Snow showers and icy stretches may cause some disruption, it said.
Temperatures across the country will become milder from Thursday.