Multiple police were at the Newtown Park Apartments on Mansfield St after the sudden death was reported.
Police today said they have concluded the post-mortem and scene examination phases of the investigation.
“Police acknowledge this is a very distressing time for the baby’s mother and the wider family, and we continue to support and work with them,” they said in a statement.
“Inquiries are ongoing to establish what happened in the lead-up to the baby’s death, and the family are fully cooperating with police.”
The Herald understands the block of apartments is owned by the Wellington City Council.
A spokesperson for the council said; “This is a police matter, and we, along with the landlord Te Toi Mahana, will assist them with their inquiries regarding this tragic incident. Our thoughts are with the whānau during this difficult time.”