Roisin Walker, 14, endured a six-hour operation on her neck and will face up to eight weeks in a neck brace.
She was hurt when a car ploughed into a group of children in Castlemilk on Saturday afternoon.
Police Scotland, which is treating the incident as attempted murder, said the teenager appeared to have been struck twice – firstly as the car was travelling forward on Stravannan Road, then again as it reversed.
Two other girls, two boys and a man - who is thought to have been the target of the car which hit the children - were treated for minor injuries.
Trisha McGonagal, Roisin’s mother, told the BBC she is hopeful her daughter will not need further surgery and admits she is lucky to be alive.
She said: “The brace will be on her neck for six to eight weeks and it will be a slow process but hopefully she will get there okay.”
“The nerves to her right arm have been damaged making that really weak and we are not sure if that will get better but if that’s all she comes out the other side with, then I’m happy with that.
“We are so lucky she’s still alive at all, the break in her neck was pushing on her spinal chord so it could have been so much worse.”
Roisin’s sister, Jamieleigh, 21, who described her sibling as a “brave wee soul”, thanked the public for their support and urged anyone with information to contact police.
She said: “They drove away without even getting out to see if she was ok. It’s disgusting. They deserve to be caught. They should not be on the streets.”
Officers are exploring a number of lines of inquiry and continuing to review CCTV footge and carry out door-to-door inquiries.