The Met Office said frequent snow showers would follow a band of rain and sleet from the north.
As cold air moves in it could lead to between a dusting of snow and several centimetres on roads and pavements, especially towards the north coast.
Icy stretches are also likely to form as overnight temperatures fall to 0C and below for some.
Wintry showers will continue through Tuesday but as temperatures rise during the day there is unlikely to be a further risk of ice and snow on lower roads.
The warning is in place from 17:00 on Monday until 11:00 on Tuesday.