The alert also applies to Clackmannanshire.
The Met Office is forecasting wintry showers will continue for the rest of the day before easing towards midnight with icy patches forming on untreated surfaces.
Snow showers will lead to a slight covering of snow in places, with a few cm possible on higher routes.
It said some roads and railways likely to be affected with longer journey times by road, bus and train services – and there could be icy patches on some untreated roads, pavements and cycle paths.
Traffic Scotland advised motorists it may lead to some tricky driving conditions.