It has issued a yellow "be aware" warning for southern and central Scotland and for parts of the Highlands and Aberdeenshire.
The warning covers from 04:00 to midday on Tuesday and follows snow and freezing temperatures that affected some areas at the weekend and Monday.
Snow could fall to depths of 5cm above 200m and 10cm above 500m on Tuesday.
The Met Office said: "Rain will move northeast across Scotland and north east England on Tuesday morning, falling initially as snow which will accumulate in places.
"Rain may also fall onto frozen surfaces for a time, which could result in very icy conditions. Snow accumulations at low-levels will vary across the warning area.
"The public are advised to be aware that there could be some disruption to travel."
Perthshire, Aberdeenshire and parts of the Highlands had snow and icy conditions on Sunday into Monday.
Snow and ice could cause some disruption on Scotland's roads on Tuesday, the Met Office has warned.