Catriona Rouxel, 38, was last seen in Perth about 3pm on Monday.
She is described as 6ft1’, of slim build, with long fair to blonde hair, which has a temporary red colour.
She wears large rings on her fingers and was last seen wearing a long brown or khaki parka style jacket, blue jeans, and red shoes.
Police Scotland said they believed Ms Rouxel may have travelled to the Edinburgh area.
She suffers from a medical condition that requires medication. Police said if she has not taken the medication, she could appear to be confused or verbally aggressive.
Anyone with information is urged to call Police Scotland on 101.