The warning comes into force at 4pm on Saturday and extends to 10am on Sunday.
The Met Office notes: “Temperatures will again fall widely below freezing during Saturday evening. This will allow ice to form readily on untreated surfaces, particularly where roads and pavements remain wet from wintry showers.
“Scattered showers will fall as a mixture of rain, sleet and snow. Most areas are unlikely to see any fresh accumulations of snow though some slight falls are possible in places, mainly over Shetland and on higher ground in North Highland.”
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Meanwhile, a yellow alert for snow and ice has also been issued by The Met Office, warning of some “potential disruption” due to wintry showers and icy patches.
The warning, covering Fife, Grampian, Tayside and parts of North Lanarkshire and West Lothian, is in force from 9am on Sunday until 6am on Monday.
The Met Office notes: “Whilst some areas will see little in the way of precipitation, showers, falling as snow away from windward coasts, will bring local accumulations of 1-4 cm. Near windward coasts, a mixture of rain and sleet is more likely.
“During Sunday evening and overnight into Monday, ice is likely to develop on untreated surfaces.”
A yellow warning for heavy snow is already in place across southern Scotland from Sunday and overnight into Monday.
The Met Office forecasts that 2-5 cm of snow could accumulate widely over parts of southeast Scotland and as much as 10-15 cm over the higher ground of the Borders.
Rain or sleet is more likely near some eastern coasts.