A Status Orange fog alert has been issued for 18 counties.
Met Eireann issued the warning as thick fog poses a threat to driving conditions across the country.
The alert is valid between midnight on Monday and 8am on Tuesday.
A spokesperson said: "Mist will thicken into fog overnight and will be dense at times."
The counties affected are: Dublin, Carlow, Kildare, Kilkenny, Laois,Wexford, Wicklow, Offaly, Westmeath, Meath, Galway, Mayo,Roscommon, Clare, Cork, Limerick, Tipperary and Waterford.
Irish weather forecast: Met Eireann predict mild week ahead as temperatures will hit highs of 15C
The early hours of Tuesday morning will be foggy, especially across parts of Leinster, Ulster and Connacht.
It will be another cold night with temperatures of as low as 3C.
A spokesperson said: "Misty and mostly cloudy overnight. Some rain at times, mainly across parts of Leinster, south Ulster and north Connacht.
"Elsewhere a mix of cloud and clear spells, with just a few patches of drizzle.
"Fog will form, mainly over the southern half of the country and will be dense in places. Lows of 3 to 7 C, in light to moderate easterly breezes."
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The national forecaster has warned of a "murky" start to Tuesday, as the fog begins to clear.
Sunny spells will form with the temperatures hitting as high as 14C, with Ulster experiencing the best of the sunshine.
"A dull, murky start in many places tomorrow. But bright and dry over Ulster.
"The mist, fog and drizzle, will clear gradually southwestwards on Tuesday, clearing south Munster later in the afternoon.
"Bright or sunny spells will develop in the clearance. Top temperatures of 10 to 14 C, in moderate easterly breezes."
Irish weather forecast: Temperatures to hit 15C today but cold frosty nights ahead this week
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