The girl, who has not yet been named, managed to call emergency services after she was attacked at about 1.20pm.
Police and paramedics treated her at the scene in the Elmfield Park area of Doncaster, before taking her to hospital.
South Yorkshire Police have since confirmed that she died from her injuries at Doncaster Royal Infirmary.
A 26-year-old woman has been arrested and remains in police custody.
Sky sources said the girl had been involved with Doncaster social services and that police and social workers had met to discuss the incident and any previous contact with her.
The park has been cordoned off and blue police tape can be seen on railings and trees.
One woman, who was passing the scene with her 13-year-old daughter, said she no longer allowed her to go into the park.
“It is not a very good park, to be honest. There have been a number of incidents in there, it is not like when I was a child.”
She said her daughter had come across a drunk woman when she was walking close to the park on Tuesday.
The teenager said: “We were just walking and we decided to run. She was walking past and she asked us why we are running. She started calling us names.”
A local shopkeeper said: “They should put CCTV cameras in the park. A few customers have been saying that.”
He added: “It is such a shock. It is really sad. You see kids playing football in the park. It is the first time we have had a stabbing around here.”
He said five or six years ago a man set himself alight in the park.