Fire and Emergency NZ crews were called just after 2am on Wednesday to the housing block Toanui St, which was well ablaze when they arrived.
About 40 firefighters from the Rolleston, Dunsandel, Kirwee, Lincoln, Wigram, Ilam and Christchurch City stations were called in to fight the fire.
Several crews remained at the scene on Wednesday morning.
Fenz shift manager Blair Walklin said multiple units were also damaged during the blaze.
“When crews arrived, the house was well ablaze. A number of attached units also suffered damage,” he said.
A scene guard was in place this morning and inquiries into the circumstances of the fire are ongoing.
The cause is unknown and a fire investigator will be at the scene this morning.
Hato Hone St John said three ambulances, two rapid response units and a manager were sent to the scene.
St John paramedics treated four patients and took three to Christchurch Hospital.
Police and the New Zealand Defence Force confirmed one person died in the blaze.
Burnham Auto Services/Challenge Service Station said on its Facebook page it is collecting donations for the local family affected by the fire.
"A very sad morning for one of our Burnham families. Our heart and thoughts are with you all.
"We are taking monetary donations for our local family for anything needed going forward. These will be held in trust for the family.
"Burnham community - this is the time to support each other and look out for one another. The true meaning of community."
While housing at Burnham Military Camp is owned by the NZDF, some is occupied by NZDF personnel and some is tenanted by non-NZDF personnel.
Houses occupied by non-NZDF families are managed through commercial property managers.
"Our thoughts are with the whānau who have lost a family member, and all of those impacted by today's fire," Richardson said.
Support was being provided to all those affected, she said.
Rangiora house fire
Firefighters have also extinguished a house fire in Rangiora.
Fenz crews were called to the scene about 4am and found the property ablaze. The house was unoccupied at the time.
The house on Southbrook Rd is connected to a homicide investigation.
The property had been searched by police investigating the death of Richard Leman, whose body was found in his car parked in a garage in Tyler Street in April 2023.
-RNZ and Star News