The incident happened at the Lidl, in London Road, North End, on Wednesday afternoon.
Pictures from the scene show the demolished brick wall at the rear of the supermarket’s car park, which is off Derby Road and runs along Pitcroft Road.
A police spokesman confirmed that a man had been arrested suspected of driving while unfit through drink or drugs.
They said: ‘Between 2.30pm and 2.45pm on Wednesday, April 14, a car collided with a wall in Lidl car park in Derby Road.
‘The car, a Vauxhall Insignia, also collided with a stationary vehicle.
‘A 60-year-old man from Southsea was arrested on suspicion of driving whilst unfit through drink or drugs.
‘He has been released from custody but remains under investigation.’