The area is cordoned off and a police tape runs across the front door of the building.
A police officer stands guard in front of the block.
Wellington Detective Senior Sergeant Warwick McKee said: "Police will be in the neighbourhood speaking to the community and residents to determine her recent movements in and around the address."
Mr McKee said officers visited the woman's house at about 7pm for a "well-being" check, and found her dead. Her death is so far unexplained.
"Arrangements are now being made to confirm her identity and to contact and notify next of kin," Mr McKee said.
Laura Gardner, who lives near the property, said she saw perhaps five police cars and a fire engine at the scene.
"I actually thought it was a drug bust or something because I could see hazard suits," she said.
At first she was unsettled but a police officer said neighbours had nothing to worry about.
"That gives me hope that maybe it's genuinely not something people outside of the incident need to worry about."
Another neighbour returned home about 9pm and saw at least five police cars and a fire engine. She saw a policeman and a fireman in full protective gear.
Anyone with information can contact Wellington Police: (04) 381 2000 or CrimeStoppers: 0800 555 111.