A dark blue Ford Fiesta was being driven by an 18-year-old woman northbound in Western Road, Sompting, when it left the road and struck a 91-year-old woman at 10.45am on Saturday, September 7.
The victim, from Sompting, was taken to Worthing Hospital for treatment for a serious injury to her right leg.
The collision happened just north of the railway bridge in Western Road, and officers are keen to speak to anyone who saw the Fiesta being driven in the minutes beforehand.
The 18-year-old, from Lancing, was arrested on suspicion of causing serious injury through dangerous driving.
She was questioned, before being released on bail until December 3, while officers carry out further inquiries.
Anyone with information should call 101 quoting Operation Helix or email [email protected]