The incident took place around 12.45pm on January 26 in Buccleuch Street when a 43-year-old male was punched to the face.
The man was taken to the Edinburgh Royal Infirmary where he received medical treatment for a serious injury
The suspect is described as male, white, 6ft - 6ft 2ins, thin build, greying hair wearing a high vis jacket and sandy coloured boots.
DC Stephen Herd of Gayfield CID said: “We’re still conducting enquiries in order to establish the full circumstances surrounding this incident and are eager to speak to anyone who may have witnessed the incident or recognise the suspect description”
Anyone with information can contact Police Scotland on 101 or report this anonymously to the Crimestoppers on 0800 555 111.