The Met Office has issued the warning for eastern Scotland from 5pm on Sunday to 12pm on Monday.
Wintry weather already caused travel disruption along the west coast on Saturday, with Glasgow Airport suspending all flights after “heavier than expected” snowfall.
ScotRail also reported some disruption due to issues with signalling systems caused by snow.
The weather service said wintry showers, with snow on hills, falling onto frozen surfaces may lead to some disruption to transport and infrastructure.
In its warning the Met Office said “occasional wintry showers will affect eastern Scotland this evening and through Monday morning, the showers falling onto frozen surfaces giving the risk of ice.
“A cm or two of snow is possible at low levels inland with 5-10cm over the hills, but showers at low levels expected to turn increasingly to rain overnight.”
Temperatures fell to as low as minus 8C in parts of Scotland on Friday evening.