His partner was shot dead by an officer after police were called to the Kāinga Ora property in Clyde Rd, in the suburb of Bryndwr, about 11pm on Wednesday following a report of family harm.
Police say the man came out of the house with a hunting knife and was shot at, after which the woman picked up the weapon and began approaching police.
A second shot was fired and the woman was hit. She died shortly afterwards.
Canterbury District Commander Superintendent Tony Hill said the man had surgery yesterday afternoon.
A scene examination was continuing and a post-mortem of the woman was expected in the coming days.
Cordons and a scene guard would remain in place at the property.
"Incidents such as this are complex and a range of investigations are already under way," Hill said.
"As such, we are limited in the detail we can provide at this stage.
"Police are supporting the family of both the man and woman, as well as our own people."
Officers involved in critical incidents such as fatal shootings were provided full welfare and wellness support, he said.
The shootings have been referred to watchdog the Independent Police Conduct Authority.
