The alert covers all of the Republic and five of the six counties in Northern Ireland.
It came into force at midnight and will remain in place until 7pm tomorrow.
Both gardaí and the Road Safety Authority (RSA) urged people to drive with care given the challenging conditions - with everyone also urged to comply with public health guidelines over the Covid-19 pandemic and the Level Three restrictions.
Met Éireann said some of the downpours will be exceptionally heavy this week.
"Persistent and occasionally heavy bands of rain will cross the country through to tomorrow evening," a spokesperson said. "While some areas will remain below Status Yellow warning levels, there is a risk of localised spot flooding with a heightened risk of flash flooding in mountainous regions."
The forecast is for a very unsettled week with spells of heavy rainfall and overnight temperatures sinking close to freezing.
"Today will be cloudy, wet and breezy. Persistent rain across the southwest early in the morning will spread to nearly all parts of the country by late morning and will be heavy at times, especially in the west and north.
"There will be a risk of river and surface flooding.
"The rain will ease across the southern half of the country for a time later in the afternoon, but further heavy rain will move in from the southwest and become widespread.
"Low pressure is currently forecast to move north-eastwards over the country during tomorrow, causing strong southerly winds in the south and east.
"Heavy and persistent rain in northern areas tomorrow morning is expected to clear away to the North during the morning, but through the rest of the day further outbreaks of heavy rain are forecast to move north-eastwards across the country as the low pressure system tracks over Ireland."
Temperatures will hover between 12C and 14C.
"Wednesday will be a cooler day with moderate to fresh northerly winds, strong along western and northern coasts and temperatures of 10C to 13C.
"Wednesday night will be cold, dry and clear with frost likely in many areas and lowest temperatures of 0C to 4C.
"There will be a bright but chilly start to Thursday morning which will be a mostly dry day with highest temperatures of just 9C to 11C."
Friday is also shaping up to be unsettled.