The 23-year-old was said to be making her way down the escalator at around 5.40pm when a male intentionally pushed her causing her to tumble almost to the bottom.
As a result she was knocked unconscious briefly and was treated by paramedics but declined further treatment.
Officers are said to be following a positive line of inquiry but are asking anyone who can assist with their investigation to come forward.
The suspect is described as white, early twenties, 5ft 6ins, with a regular build, short flat black hair and pale skin. He was wearing a white polo shirt, blue tracksuit bottoms and trainers.
Sergeant Dave Hughes said: “This was an unprovoked assault, could have had far more serious consequences and left the victim with more serious injuries.
“The Princes Street and Waverley Station area are always extremely busy and there would have been several members of the public around who may have witnessed this incident.
“I would therefore ask that anyone who can help us with our ongoing inquiry contacts police immediately.”
Those with information can contact Police Scotland on 101 or alternatively the charity Crimestoppers on 0800 555 111