The incident happened at around 11am on Friday, 19 January outside the Salisbury Road Surgery on Salisbury Road.
The victim, a 95-year-old man from Southsea, was walking along the pavement pushing a walking frame, when he was in collision with a Volkswagen Passatt.
He suffered life threatening injuries and is currently at the Queen Alexandra Hospital.
Sergeant Mark Furse, said: “I am appealing for anyone who witnessed this incident to come forward and speak to us. If you have any information, please call us on 101 quoting 44180024771.”
A 33-year-old man from Cleveland has been arrested on suspicion of causing serious injury by dangerous driving, attempting to pervert the course of justice, failing to provide a specimen, and driving whilst unfit through drink or drugs. He has been released from custody but remains under investigation.
If you have any information relating to this case, please call 101 quoting reference '44180024771', or contact Crimestoppers anonymously.