The crash happened in East Parade, outside the Victoria multi-storey car park, at about 1.20pm yesterday (Thursday).
Police said it involved a silver Skoda Fabia estate car, which was exiting the car park, and a black Vauxhall Corsa travelling along East Parade.
The driver of the Skoda, an 85 year-old woman from Harrogate, was taken to Harrogate District Hospital.
She has since been transferred to Leeds General Infirmary with life threatening injuries.
The driver of the Vauxhall, a 30 year-old woman from Wetherby was also taken to Harrogate District Hospital with minor injuries and was later discharged.
Officers investigating the collision have issued an appeal for witnesses to the crash to come forward.
Anyone with information is asked to call police on 101, quoting reference number 12180086388.