The 23-year-old had been out with friends in Fredrick Street on Saturday evening and was walking along St Vincent Street at around 2.40am on Sunday morning when she was targeted.
The woman struggled with her attacked and began to scream loudly. He then made off along North East Circus Place towards Stockbridge.
Two members of the public then came to the woman’s aid and she returned home before contacting police.
Officers believe this incident was sexually motivated and are investigating whether it could be linked to a similar incident, which happened in Cumberland Street in the early hours of Saturday, September 29.
On that occasion a 29-year-old woman became aware of a man running up behind her. He grabbed her mouth and dragged her backwards a short distance before she was able to shout for help and the attacker fled.
There is currently no description of the suspect from Sunday’s attack but anyone who was in the area and remembers seeing anything suspicious is asked to come forward.
Chief Inspector Gavin Phillip said: “This was a terrifying ordeal for the young woman to endure and fortunately she was not seriously injured as a result.
“Her screams would have undoubtedly been heard by local residents, who may have information that can assist with our enquiries.
“Similarly, people making their way home at the time may have seen the woman as she walked home, or noticed her attacker in the area prior to the assault.
“As part of our enquiries, we are reviewing the circumstances of a similar incident in Cumberland Street at the end of September.
“High-visibility police patrols will be out in the area to engage with members of the public and offer local reassurance to the community.
“Anyone with information relating to either of these assaults should contact police immediately.”
Those with information can contact Lothian and Borders Police on 0131 311 3131, or the charity Crimestoppers in confidence and complete anonymity on 0800 555 111.