The incident took place at the Day-Today Store on Boswall Parkway just before 3am.
Witnesses described how the robbers wearing balaclavas forced the premises’ shutters open, broke the window before making off in a grey or silver medium sized hatchback car along towards Crewe Road North, in the north of the Capital.
DCI Paul Grainger said: “The audible alarm was activated and their actions would’ve caused some noise at this time of the morning.
“We are looking to speak to anyone who heard anything or saw the incident or anything suspicious, or the car driving off.
“We believe that a black people-carrier type private taxi may have driven by as this incident happened. I would urge the driver or passengers to get in touch with us.”
Anyone with information is asked to contact Police Scotland on 101 quoting incident reference number 0689.