Temperatures are expected to plummet to minus four overnight.
Road users have been warned to take extra care as severe frost and patches of freezing fog develop across the country.
Met Eireann warned Monday night will also be very cold, leading to very frosty conditions and icy stretches.
The Road Safety Authority (RSA) the early part of the week will be cold, with extensive night frosts occurring in most places, while it could snow later in the week in northern and eastern counties.
It urged road users to slow down as fog and frost may not clear in some areas during daylight hours.
Motorists should be particularly aware of the risk of black ice on the roads and freezing fog.
"Visibility is greatly reduced in such conditions," it said.
"A collision involving one vehicle can quickly involve many others, especially if driving too fast and too close to the vehicle in front.
"The greatest risk is of a multiple-vehicle pile-up on roads with higher speeds such as motorways and dual carriageways."