The woman is understood to have been found at around 6am in Pilrig Park with serious cuts and bruises to her face and ripped clothing.
The circumstances surrounding the violent assault are not yet known, but the 23-year-old victim is now recovering in hospital.
The attack came just hours after reports that a teenager was sexually assaulted in the city centre. Police said they were not linking the two incidents.
Police officers, detectives and forensics yesterday spent the day scouring the cordoned-off play area in Pilrig Park for clues as to the nature of the attack.
Around a dozen police officers carried out a full search of the nearby grass area and detectives were seen during the afternoon taking prints from the area around the park’s slide.
A resident who lives nearby the park said she hadn’t heard anything that night.
She said: “We had the windows open but we didn’t hear anything. It seems like something serious has happened. A local dog walker told us he was walking his dog at around 4.30am and he didn’t spot anything at all, so it might have happened later.”
A nearby shop worker told the Evening News that a woman had come into her shop with news that the victim had been spotted with a badly “bust-up face” and ripped clothing at around 6am.
She said: “A friend of a woman who came into the shop had said the girl had been seen with cuts and bruises all over her face.
“Her clothes were apparently ripped and she looked in a bad state.
“She said her face was all bust up, which is really quite shocking to hear.”
A police spokesman said officers were investigating the serious incident.
He said: “Lothian and Borders Police are investigating after a 23-year-old woman was found within Pilrig Park at around 6am on Sunday 22nd July having sustained serious facial injuries.
“She was taken to hospital where she continues to be treated.
“Inquiries are ongoing to determine the circumstances surrounding this incident.
“Anyone who can assist officers with their investigation is asked to come forward immediately.”
Local Leith/Links community council chair Jim Scanlon said the attack was concerning.
He said: “It’s a serious concern that this kind of thing could happen around there, especially at that time of the morning when there would be potentially few witnesses about. Hopefully police will get to the bottom of it.”
Just hours before the park attack a sexual assault was reported to have taken place in the city centre, at Fishmarket Close.
The area was sealed while detectives investigated a potential incident involving a 19-year-old woman at 3am.
A spokesman said: “Lothian and Borders Police responded to the Fishmarket Close area of Edinburgh following a report of sexual assault on a 19-year-old woman.
“Officers continue to investigate the full circumstances of this incident, which happened around 3am on Sunday 22nd July.
“Anyone who was in the area of the incident in the early hours of Sunday and remembers seeing anything suspicious is asked to contact police immediately.”