The weather service says icy patches are expected to form on untreated roads, pavements and cycle paths from 5pm on Sunday night until around 10am on Monday morning (February 11-12).
A spokesperson said this is likely to lead to some injuries from slips and falls.
The chief forecaster said in a statement: “The cold conditions with a mixture of clear spells and wintry showers will continue through Sunday night and Monday morning.
“This will result in temperatures falling rapidly on Sunday evening and icy patches developing on untreated surfaces, especially where any wintry showers lead to wash off of previous treatment.
“Any heavier snow showers may lead to temporary accumulations of 1cm or less at low levels whilst over higher ground, above approximately 200m, as much as 2 to 5 cm may accumulate in a few places.”
For more information visit the Met Office website here.