Officers are looking into the robbery in the Stenhouse area of the Capital which took place at around 12.15pm on Tuesday, September 12.
The man is described as white, 5ft 10ins to 6ft tall with a slim build. He was wearing a quilted jacket, dark trousers and white Adidas trainers.
Detective Constable Kevin Walls said: “While the shop worker was not injured, this was a frightening experience, which resulted in the theft of goods from the store.
“Anyone who remembers seeing any suspicious activity around Nadeem Store, 10 Stenhouse Cross, Edinburgh, should contact police immediately.”
Those with information can contact Police Scotland on 101 or make an anonymous report through the charity Crimestoppers on 0800 555 111.