Police and paramedics spent several hours at Barkis House, Brownlow Close, Landport, on Wednesday afternoon.
A spokesman for Hampshire Constabulary confirmed a 44-year-old woman had been found dead but there were no suspicious circumstances. A file has been passed to the coroner.
A long-term resident of the high-rise block said: ‘We wondered what was going on as the police were there for a long time. It’s sad that a woman has died. Forty-four is no age.’