Homicide detectives say 22-year-old Chozyn Koroheke, who died at a house in Auckland's Pakuranga Heights on Tuesday night, was shot at close range with a shotgun.
Detective Senior Sergeant Kevin Tiernan said they were searching for Ms Koroheke's boyfriend, Turiarangi Tai, in connection with her death.
A firearm was found at the scene, but it was not clear if this was the weapon used.
Ms Koroheke's death was a "complete tragedy" for her family, Mr Tiernan said.
"A 22-year-old woman has lost her life and her family is grieving for her. Police and Victim Support are supporting them through this difficult time."
Mr Tai, 22, should to do the right thing and get in touch with police. Anyone helping him hide could face arrest, Mr Tiernan said.
Emergency services were called to the house on Tuesday. Ms Koroheke had serious injuries and paramedics could not save her.
Police said they were trying to establish exactly what had happened, but believed it was a domestic-related incident.
Mr Tai, who had links across Auckland, Waikato and the Bay of Plenty, had nine warrants for his arrest for charges including unlawfully taking a motor vehicle, dangerous driving, wilful damage and failing to stop for police, Mr Tiernan said.
"These are not related to the homicide investigation," he said.
Ms Koroheke's friends have posted tributes on social media.
One said: "Your kiddies need their mum ... and darling you deserve justice."