The collision happened at 1.50pm on Nyetimber Lane at the junction with Carlton Avenue and involved a red Renault Clio and a red Kia Venga, a spokesman said.
They added the driver of the Kia, a 73-year-old woman from Bognor, was taken to St Richards Hospital but there were no reports anyone else was injured.
Anyone with information is asked to contact police on [email protected] quoting serial 669 of 20/03.