Kirstie Walford's daughter Riannon was crossing Firshill Crescent, in Pitsmoor, last Wednesday (January 11) morning when the collision happened.
The 10-year-old escaped with only bruises, but the scare has prompted a campaign for new road signs at the zebra crossing outside St Catherine's Catholic Primary School, which she attends.
"Luckily she's OK now but we're really shaken up. It could have been a lot worse and they need to do something to improve safety there," said Kirstie.
Riannon's grandmother Jean Conneally said: "She was crossing the road with her two younger sisters when she was flung off the bonnet of a car.
"Her arm's in a sling but thankfully it's not broken. The traffic is quite bad there and many drivers don't seem to realise there are children crossing, which is why they need new signs."
The petition was started by Pauline West, a 78-year-old grandmother who lives on Firshill estate and attended the school as a girl.
"Luckily Riannon wasn't seriously injured but there have been a number of near misses before now and we don't want to wait for a horrific accident before something is done," she said.
"I've been asking for years for proper signs to warn drivers that children are crossing, because the way some people speed down here is incredibly dangerous."
The Star recently revealed how the number of lollipop people helping schoolchildren cross the road safely in Sheffield had fallen from 79 to 58 over the last four years.
Sheffield Council said it is introducing more 20mph zones and teaching children how to travel to school safely.
Councillor Mazher Iqbal, cabinet member for transport and infrastructure, said: "School safety is an absolute top priority for the council. We were concerned to hear about this incident outside St Catherine's and relieved to learn that the girl involved wasn't seriously injured.
"This week we have been delivering training in the school to ensure that children act safely when travelling to and from school.
"We look forward to receiving this petition from parents. Once received our officers will fully investigate the issues raised in the petition which will include a review of the signage at the school to see if more can be done to ensure road safety.
"As a council we’re introducing new 20mph zones – and will soon announce more – and speed indicating devices have been introduced which will make our roads across the city safe.”
Police said a child had been involved in a collision with a driver, who failed to stop at the scene but had since been traced and interviewed by officers.
Anyone with information is asked to call police on 101, quoting the incident number 254 of January 11.
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