Police were called at around 6.42am on Monday after the victim was found in the road on High Street outside of the Duke of Buckingham pub.
She had suffered injuries to her head, arms and knees.
She was taken to Southampton General Hospital where she later died.
Her family have been informed and are being supported by specialist officers.
Police have said that subsequent enquiries have revealed that the lady was struck by a black Nissan Qashqai, which didn’t stop at the scene.
A 45-year-old man from Portsmouth has been arrested on suspicion of causing death by dangerous driving, committing an act/series of acts with intent to pervert the course of public justice and being the driver of a vehicle involved in a road accident that failed to report that accident.
He remains in police custody at this time.
Hampshire Constabulary said in a statement: ‘We would like to hear from anyone with information that may assist our enquiries. Were you in the area at the time?
‘Did you see or hear what happened, the moments leading up to it or the aftermath? Perhaps you were driving through the area and may have dash cam footage or maybe you live nearby and have Ring Doorbell footage that may assist our investigation?’
Anyone with information is asked to call 101 quoting 44220020934/Op Nebulous. Alternatively, go online and submit information via the following form: https://www.hampshire.police.uk/tua/tell-us-about/cor/tell-us-about-existing-case-report/