Police officers were called to Cuckmere Lane shortly before 3pm on Thursday, where a large emergency response was called to a 25-year-old woman found with serious injuries.
She was taken to hospital and died on Friday, August 29, with her family now being supported by specialist officers.
READ MORE: Tributes to Southampton woman who died after falling from flats
A homicide investigation was launched and an 18-year-old man from Southampton has now been arrested on suspicion of murder as part of the investigation, Hampshire police have confirmed.
A spokesperson said police are not looking for any further suspects at this time.
Floral tributes have been placed outside a block of flats in Redbridge in the days since the incident in memory of the woman.
One letter said: “Thank you for always being proud of me.
“Thank you for being the best big sister ever. You were the smartest person I ever knew, and I’ll forever be proud of you.”
Officers are continuing to patrol the area.