The 19-year-old woman was walking through the Meadows area at about 3:30am on Tuesday when she was grabbed by two men, police said.
Officers are appealing for witnesses to the sexual assault, which happened in an area north of Melville Drive.
Both suspects are described as white, in their 20s and of average build. They were wearing dark-coloured hooded tops and made off towards Bruntsfield Road.
A police spokesman said: “Although we know that the assault took place in the Meadows, we are still working to establish exactly where it happened and we are appealing for any information that can assist our inquiries.
“Anyone who was in the area of the Meadows or Bruntsfield Links in the early hours of [Tuesday] morning who saw or heard anything suspicious should contact police immediately.
“Similarly, anyone who saw two men matching the descriptions of the suspects in either the Meadows or Bruntsfield Links areas should also get in touch.”
He added: “At this time, we have put in place extra patrols in the Meadows area overnight in order to provide reassurance to the public.”