A group of five teenage boys set a 13-year-old girl's hair and arm on fire in a park in a "shocking and completely unprovoked incident", police said.
Cambridgeshire Police said the girl was attacked at the recreation ground in Normanton Road, Peterborough at about 14:00 BST on Sunday.
The girl's arm and hand were burnt as she tried to put out the fire.
Det Con Leeza Phillips said: "It was incredibly traumatic for the victim and has left her in a lot of pain."
An ambulance was called and the girl received treatment nearby.
The suspects were described as white, about 15 years old, wearing dark clothing with one of them carrying a backpack.
After the incident, they ran off in the direction of Parnwell, police said.
Det Con Phillips said: "This was a shocking and completely unprovoked incident.
"Her injuries could easily have been even worse.
"I'm appealing to anyone who saw what happened, or has information, to contact us."