Shona Priestly was last seen at an address in Craigentinny Road on Friday morning and has not been in touch with family or friends since Friday afternoon.
The 35 year old is described as white, around 5 foot tall, of slim build, with light blonde hair which is usually tied in a bun. She has a distinctive tattoo of a name and flowers on one hand.
Posting on Facebook, police in Edinburgh said: “Shona was last seen wearing a black full length dress with white flowers and black shoes which tie at the ankle.
“It’s believed Shona may have travelled to Oxford.”
Inspector Grant McCulloch of Craigmillar Police Station said: “Shona has health concerns and we’re growing increasingly concerned for her welfare given that she has been missing overnight.”
“Anyone who may have seen a woman matching Shona’s description since this time, or has any information that can help us trace her, is asked to get in touch as soon as possible.”
Those with information can contact Police Scotland on 101, quoting incident number 3318 of 23 June.