The Met Office has warned that there is a small chance of flooding.
The yellow warning will remain in place until 9 am on Tuesday.
A Police Scotland spokesman said: “Please take care if you are out and about.
“Leave extra time for any journey you are making and expect standing water on the roads.
“Please switch your vehicle lights on and remember stopping distances increase on wet roads.
“Pay particular attention for vulnerable road users such as cyclists and pedestrians.”