The 59-year-old was crossing Osborn Road, just south of the Ashcroft Arts Centre, when she was involved in a collision with a car.
She was taken to Queen Alexandra Hospital, in Cosham, following the incident around 12.30pm.
The car was described as a red Nissan Micra or similar and the driver was described as an elderly man.
PC Peter Sarginson, from the Havant Roads Policing Unit, said: ‘We would like to hear from anyone who saw this incident or can assist us with identifying the vehicle and the driver.
‘This area would have likely had a constant flow of traffic and occasional pedestrians using the footpath so it is likely someone saw what happened.
‘We are particularly keen to trace a woman who we believe has useful information but who had already left the area by the time police arrived.
‘I would urge the driver to come forward so we can establish exactly what happened.’
Anyone with information should call Havant RPU on 101, quoting 44170287271.