High winds and showers of sleet and snow are expected to hit much of the country, forecasters have said.
A weather warning was issued by Met Eireann, which said strong to gale force westerly winds will produce gusts of 110km/h to 130km/h in Connacht and Donegal on Monday.
Elsewhere, Munster, Leinster, Cavan and Monaghan are expected to have 90km/h to 110km/h winds.
The Road Safety Authority (RSA) has advised motorists to take care, particularly those in high-sided or vulnerable vehicles.
Met Eireann said it will be extremely windy with some severe, possibly damaging gusts.
"After dark, heavy wintry showers of hail, sleet and snow will develop at first in the north of the country, but during the night they will become more widespread and produce some accumulations of snow, in particular on high ground but also at lower levels," it said.
"The very strong winds and snow showers will produce some blizzard-like conditions especially on higher ground, with icy patches at all levels. The wintry showers will turn to rain showers on Tuesday afternoon as temperatures increase."
The RSA urged drivers to be aware of falling debris on the road and vehicles veering across the road driving in wet and windy conditions.
It said road users should be aware of the danger of aquaplaning, especially on roads, and to leave extra space between other vehicles.
"Pedestrians and cyclists are advised to be seen," the RSA added. "Take extra care when near traffic or crossing the road in extremely windy conditions as sudden gusts can blow you into the path of an oncoming vehicle."