The crash, involving silver Skoda Octavia taxi, happened on Lake Road at 00:30 BST.
Police said the pedestrian, a 20-year-old woman from Fareham, died at the scene.
A 37-year-old man, from Portsmouth, has been arrested on suspicion of causing death by driving without due care and attention.
He has been released from custody but remains under investigation, Hampshire police said.
Anyone who witnessed the crash or saw the woman or the taxi beforehand has been urged to contact police.
A woman died when she was struck by a taxi in Portsmouth.