Police are appealing for witnesses after the incident in Fountainbridge at 1am on Sunday.
The 35-year-old woman was spat at and then assaulted by a man outside the Casino building.
A 48-year-old man intervened and was subsequently punched in the face by the suspect.
The Scottish Ambulance Service attended and the man was taken to the Edinburgh Royal Infirmary for treatment.
Inquiries are ongoing to trace the suspect and anyone who can assist with the investigation is asked to come forward.
He is described as a white man, aged in his late teens to early 20s, with short brown hair. He was described as wearing a denim jacket, black jeans and black shoes.
Sergeant Chris Richardson from Wester Hailes Police Station said: “This was an unprovoked attack which led to two people sustaining minor injuries.
“I am eager to speak to anyone who was in the area in the early hours of Sunday morning and who witnessed what happened.
“Equally anyone who recognises the description of the suspect, or has any information relevant to our investigation, is asked to get in touch.”
Those with information can contact Police Scotland on 101, quoting incident number 0367 of 27 May, or report this anonymously to Crimestoppers on 0800 555 111.