The woman was seen at around 5.10pm on Saturday crossing Corstorphine Road from Balgreen Road and witnesses said she appeared to be distressed.
She was without shoes and walking in the direction of Corstorphine Hill.
She is described as being of Indian/Asian origin, in her late 20’s or early 30’s with dark shoulder-length hair. She was wearing dark grey trousers, a pink long sleeved top and had no other possessions.
Police are keen to trace the woman as soon as possible to confirm she is safe and well.
Inspector Alan Bowie said: “It is not clear if this woman was hurt or in need of assistance but we are concerned given the fact that she was seen walking without shoes during today’s very cold weather.
“I would urge anyone who saw her or who can help with our enquiries to please contact police on 101 or speak to any officer.”