Three men entered the A&A Discount Store in Niddrie. One of them shouted insults and hit the owner with what appeared to be a metal chain.
Police said the 53-year-old was not seriously hurt but had been left very shaken by the attack on Tuesday.
Officers are seeking a white man in his early 20s who was wearing a white top and blue tracksuit bottoms.
He has blonde hair and is about 5ft 6ins. The incident happened at about 1100 BST at the store on Magdalene Drive.
A Lothian and Borders Police spokeswoman said: "We believe the suspect may live locally and would encourage anyone who recognises his description to come forward.
"This sort of behaviour is not tolerable in today's society. Fortunately the victim was not seriously hurt but he has been left very shaken by the incident."
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