The youngster, whose family did not wish to be named, is from Gawber and attended the long-running summer holiday funfair at Penny Pie Park, off Dodworth Road, which is operated by Scott Pullen and Son.
She was on Superspin, a ride with a rotating pole with three arms attached. At the end of each arm is a smaller rotating hub with two gondolas that somersault.
A recording of the ride shows it starting, although less than a minute the later the girl is shown being thrown from the ride before she collided with a light, speaker and fencing.
Paramedics were called to the scene and the girl was taken to hospital, suffering bruising and damaged teeth.
The girl’s family said: “We are very, very lucky that she only sustained the injuries that she did if she had been older or it was an adult that had flown off the ride, we think the injuries would have been a lot worse.
“She was sat on the row of seating by herself. She recalls the the bar going forward and sending her sideways. She tried to hang on and shut her eyes.
“The next thing she remembers was being flung into the air and hitting a light. She then hit a speaker and flew into fencing, before falling six feet to the grass.
“We are grateful that she didn’t land on a pavement because that as well would have probably caused a lot more serious damage.”
The youngster was taken to hospital via ambulance, before she was discharged several hours later.
“Since the incident she has been sleeping with her mum, firstly due to her feeling queazy but also because she is not really sleeping at night,” the family added.
“She went to the emergency dentist on Monday but apart from that she just has an awful lot of bruising. The way the staff handled the whole situation was very professional.”
Scott Pullen and Son issued a statement after the incident confirming that it had taken place and the ride had been closed, pending an inspection by the Health and Safety Executive (HSE).
“We are aware of the incident and have kept in contact with the family involved,” it said. “The ride is currently closed and will remain closed until the outcome of the HSE report and it’s given the green light.
“The family who run the ride have a very good reputation within the business.”
A spokesperson from Barnsley Council added: “We are aware of an incident that occurred at the funfair on Saturday at Penny Pie Park.
“It is being investigated by the HSE. Event organisers who use council land to host their events are required to submit an application and provide relevant documents prior to opening.”
A HSE spokesperson said: “We are investigating this incident. As this is ongoing, we cannot comment further at this time.”