The 26-year-old was approached by the thief, who said he had a weapon, at around 5pm.
She handed over her purse containing bank cards and cash before the man made off eastwards on Fettes Row towards Royal Crescent.
He is described as white, in his early 40s, around 6ft 2ins tall, heavy build, with a shaved head.
He was wearing a ski-style jacket, with a red and orange triangle design, and was a carrying a blue plastic bag. It is possible that he spoke with an eastern European accent. Although he threatened the victim with a weapon, it was not seen.
A police spokesman said: "Thankfully the victim was not injured, however she was shaken as a result of what happened, and we are appealing for any information that can assist in tracing the suspect.
"Anyone who was in the area of Fettes Row or Royal Crescent around 5pm yesterday, who saw the suspect there, should contact police immediately. Similarly, anyone who recognises his description should also get in touch."
Anyone with information should contact Lothian and Borders Police on 0131 311 3131, or Crimestoppers in confidence and complete anonymity on 0800 555 111.