Police said they were “following a positive line of inquiry” after the horrific sex assault in West Pilton Park between 11pm and midnight on Tuesday.
Officers have been combing the area for clues after taping off the park.
Forensic experts in white suits were examining a roundabout and other play equipment while items of clothing could be seen lying on the ground.
Neighbours said they had been left “shocked and worried” by the attack, after many woke up yesterday morning to the sight of police officers patrolling the area.
Mum-of-two Michelle Rintoul, who has lived in West Pilton most of her life, said she was frightened to let her own children out of the house.
The 40-year-old said: “I can’t rest my head at night until I get a phone call from my kids to tell me they are safe or I hear them coming home – and this is exactly why.
“People should be able to feel safe in their own communities but when things like this happen you don’t.
“I’m shocked this happened where it did to be honest, because it’s such a communal area and everyone knows each other.
“But unfortunately I didn’t see or hear anything.”
Michelle’s daughter, Louise, 18, added: “I can’t believe this has happened so close to home, that poor girl must be traumatised.
“It’s absolutely disgusting and I hope whoever has done it gets caught right away.”
Another resident, who lives in the high-rise flats next to the park and did not wish to be named, also expressed his shock. He said: “There’s no denying that there is a lot of crime in this area, but this is on another level.
“I saw all the police officers and wondered what on earth had happened.”
Deputy Lord Provost and local councillor Steve Cardownie said: “This is a terrible thing to have happened and it will have a traumatic effect on the victim.
“The worrying thing is that the perpetrator may strike again so I would encourage anyone who has any information about this, no matter how trivial it may be, to get in touch with the police.”
Police called for anyone with information to come forward.
A spokesman for Police Scotland said: “Police are currently investigating the serious sexual assault of a 16-year-old female, which took place at a playpark in the West Pilton Park area on Tuesday. Officers are currently following a positive line of inquiry in relation to this, but would appeal for anyone with information to come forward.”
He added: “Anyone who may have been in the area between 11pm and midnight is urged to contact Police Scotland on 101 or contact Crimestoppers anonymously on 0800 555 111.”