The incident happened around 9.05 p.m. on Monday at the Premier Convenience Store in Angle Park Terrace.
A 25-year-old man was serving a female customer when a male entered and presented the weapon before demanding money.
He then made off towards Fountainbridge with a three-figure sum of cash from the till, which he put into a black laptop bag.
Inquiries are continuing to trace the male responsible and anyone with information that can assist officers with their investigation is asked to come forward.
The suspect is described as white, around 30-years-old with a medium build, blue eyes and a light strawberry-blond beard. He was wearing a navy blue hooded top with white drawstrings, distinctive yellow gloves and a balaclava-type garment on his face.
Detective Sergeant Robbie Wallace from Corstorphine Police Station said: “Neither the staff member, nor the customer were injured during this robbery, but both were left extremely shaken and we are eager to hear from anyone who was in the area at the time and remembers seeing anything suspicious.
“We have a very detailed description of the suspect and I would ask that anyone who believes they may have saw this male, or who knows where we can locate him, to contact police immediately.
“In addition, anyone with any further information relevant to this investigation should also get in touch.”
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