The 23-year-old victim was approached by a man who spoke to her before pushing her to the ground where a struggle took place.
The suspect then fled, running towards the A701.
He is described as white, 6ft tall, in his 30s, with a local accent, and wearing a black hooded top with the hood up, denim jeans, and white trainers with stripes.
The attack took place in Castlelaw Crescent at 2.40am on Sunday.
A Lothian and Borders Police spokesman said: “The victim sustained minor injuries to her face and leg during this attack and has been left shaken as a result of what happened.
“Anyone who was in the area of Castlelaw Crescent around the time of the incident, who either saw what happened, or noticed the suspect in the area, should contact police.”
Anyone with any information can call 0131-311 3131, or make an anonymous report through Crimestoppers on 0800 555 111.