The 19-year-old victim became aware that a man was inside the property in Pier Place at about 12:15 on Friday.
A struggle between the pair resulted in the woman suffering a dislocated elbow and a minor injury to her face.
She fled and got help from a neighbour who contacted police. The suspect was thin, about 6ft and wore a tracksuit.
He also spoke with a local accent.
Police are conducting local enquiries to trace the man and asked anyone who can help identify him to come forward.
Det Sgt Mike Leask said: "The victim sustained painful injuries to her arm and face, which required medical attention and left her incredibly shaken."
A woman has been injured by an intruder during a break-in at her Edinburgh home.