This latest culling will bring the total number of chickens killed at a single Mainland Poultry property in Hillgrove, Otago, to 160,000.
Ministry for Primary Industries chief veterinary officer Dr Mary van Andel said testing and monitoring showed high pathogenic avian influenza remained confined to the farm and had spread itself within.
"As expected, a third shed on the Hillgrove property has tested positive for HPAI and its 40,000 chickens will be depopulated in the coming days.
"A fourth shed, with 40,000 chickens, is yet to test positive but we are planning to depopulate it as it is highly likely to be infected."
Continued monitoring and preliminary test results showed no infection on five other Mainland Poultry properties linked to the Hillgrove farm, where depopulation continued, Dr van Adel said.
The farm remained under strict biosecurity lockdown.
There are no reports of sick poultry elsewhere in the country.
"There remains no risk to eggs and chicken supply in New Zealand given the size of the national flock, nor any issues for food safety and human health."
