Police are appealing for witnesses to the accident, which happened at 3pm, on the A27 westbound, Upper Brighton Road, close to the entrance to Grove Lodge vets, in Worthing.
The collision involved a grey Renault Clio, driven by a 78-year-old local man, which mounted the pavement and collided with the woman, before crashing into a roadside traffic sign. The driver was unhurt.
The woman, from Storrington, was taken to the Royal Sussex County Hospital, Brighton, where she is receiving treatment.
Anyone who saw what happened or noticed the Renault shortly before the incident is asked to phone Sussex Police on 101 or email [email protected], quoting Operation Northland.