Susan Allan, aged 66, had been pushing a 10-month old baby girl in a pram at the time of the collision on Church Avenue.
The child was taken to Leeds General Infirmary with minor injuries.
A dog that the woman was walking was also injured and was taken to vets for treatment.
Police are now appealing for any witnesses to Wednesday’s incident to come forward.
At about 3.30pm a Volkswagen Tiguan was travelling north along Church Avenue and passed the junction with Long Row, outside the Brownlee Arms public house, when it failed to negotiate the bend and was involved in a collision with the victim on the offside footpath.
The driver of the Tiguan, a 43-year-old man, was arrested at the scene on suspicion of causing death by dangerous driving. He was later released under investigation.