The raid took place on the evening of Sunday 15 April at the Scotmid on Walter Scott Avenue in the Capital’s Inch area.
A three-figure sum of cash was said to have been taken by a man wielding what appeared to be a handgun.
The weapon was not discharged and no-one was injured, with police unable to confirm if the firearm is genuine or not.
A 42-year-old man is expected to appear at Edinburgh Sheriff Court on Monday.
A Police Scotland spokesperson said: “Detectives would like to thank the public for their support during the investigation.”