Met Éireann is forecasting Arctic conditions for the middle of this week which could see sleet and snow in places.
It says it will turn bitterly cold from Wednesday through to Saturday with strong winds, scattered showers and ground frost.
Severe weather has claimed the lives of more than 20 people across central and eastern Europe.
The weather system will move southwards and by Thursday showers will become increasingly wintry.
Forcasters say there will be "a noticeable change" as very cold air moves in from the north-west.
The #Jetstream will bring unsettled weather this week, moving southwards from midweek bringing #cold #Arctic air and the risk of #snow pic.twitter.com/6kMpEY4Cmo
— Met Office (@metoffice) January 8, 2017
Scattered showers will become increasingly wintry with sleet or snow likely - mainly in parts of Ulster and Connacht.
Frost will also develop in many areas also.
Lowest temperatures of between -1 to +1 are forecast.
It says Thursday will be "a bitterly cold day", with temperatures only rising to between 3 and 6 degrees in moderate to fresh westerly winds.
There will also be a mix of sunny spells and scattered wintry showers, most frequent over the western half of the country.
With #cold air on the way temperatures will take a tumble this week and with a strong northerly wind there will be a significant #windchill pic.twitter.com/g1l5QGZhT6
— Met Office (@metoffice) January 8, 2017
The highest risk of snow will be in the morning and during the evening and night.
Friday will continue to be very cold with sunny spells and further showers of rain, sleet and snow.
Temperatures will again reach between 3 and 6 degrees with westerly breezes.
While there will also be a sharp frost on Friday night.
The weekend will continue very cold with further showers of rain, sleet or snow and with sharp or severe frosts at night.