A woman and a one-year-old boy were also hurt in the collision on Holwell Road, near to North Point Shopping Centre, at around 8.30am yesterday.
Police said the woman was pushing a pram across the road when a white Citroen Berlingo van collided with her, the pram and the girl.
A Humberside Police spokesperson said: "The little girl has serious injuries and has been taken to Leeds General Infirmary, where she’s undergoing treatment. A one-year-old boy in the pram sustained bruising to his head. He’s also been taken to hospital for observation. The woman sustained minor injuries.
"The van driver has been questioned by officers but has not been arrested. The investigation is continuing."
Witnesses to the collision are asked to call the police on 101, quoting log number 90 of January 15.