Firefighters assisted with scene safety after the road traffic collision in Cakeham Road at 10.28am.
A West Sussex Fire and Rescue Service (WSFRS) spokesman added: "One engine was sent to the scene. On arrival, it was established a vehicle had collided with a single storey building.
"The crew carried out a full internal structural search of the building and the scene was made safe. Advice was given and the incident was left with the building manager. We left at 11.19am."
Sussex Police constable Tom Van Der Wee was on the scene with the county fire service and East Wittering Fire and Rescue Service.
PC Van Der Wee said: "We were called to the East Wittering medical centre to a report of a vehicle colliding with the side of a building.
"We arrived and liaised with WSFRS. A vehicle was seized and a female, aged in her 80s, is currently under police investigation."