The incident happened today in Ferrybridge Road outside The Vale Primary School at around 12.40pm, police said.
A woman in her 40s was stood at the back of her car, a Mini Countryman, when a Mercedes C-Class collided with the vehicle.
The Mini then shunted into the car in front, a Renault Scenic, which then collided with a Citroen C3.
The was taken to hospital with serious injuries.
Enquiries are ongoing.
Anyone who witnessed the collision or has any dashcam footage are asked to contact the police via 101 quoting log number *773 of December 6.