Benton Marni Parata, 44, was attacked by several inmates in his cell at Christchurch Men's Prison's high-security Rawhiti unit last month.
He was hospitalised with serious injuries and put on life support at Christchurch Hospital, but later died.
The closures will save around $20 million, plus capital costs of up to $145 million had the units remained open.
"I understand that this proposal may be unsettling for affected staff but Corrections will have extensive support and assistance in place should the proposal go ahead," Corrections Minister Peseta Sam Lotu-Iiga said.
"Prisoners have a much better chance of successful rehabilitation in modern facilities where they have access to education, training and employment."
The Department of Corrections said the closure of the prison units will coincide with the opening of the new 960-bed Auckland South Corrections Facility.
The new prison at Wiri, South Auckland will be run by private company Serco.
Overall, the number of beds for prisoners will increase by 433 this year, the department says, however, most of the 250-plus jobs at the new Auckland prison are already filled.
Corrections will help affected staff move to other prisons, where there are vacancies, if they wish.
Corrections Association industrial officer Beven Hanlon said today's announcement was, put simply, the privatisation of corrections jobs.
"This Auckland prison...the Government committed to this in the worst recession this country has ever seen. It was a $900 million commitment.
"We didn't need the prison at the time. We said that at the time. We said, if they build this prison it will cost public service jobs. And this is the second round of losses that we have had because of it."
On the suggestion that workers could move and find work at other prisons, Mr Hanlon said those vacancies reflected a "staffing crisis".
Corrections said a final decision on job losses will be made until next month.
Mr Lotu-Iiga said the proposed closures and investment in new facilities were a "step forward in ensuring our facilities are safe, secure and up-to-date".
"Prisoners have a much better chance of successful rehabilitation in modern facilities where they have access to education, training and employment opportunities.
"The new Auckland South Corrections Facility is an example of the type of facility Corrections needs to help prisoners achieve this."
Mr Lotu-Iiga said it made sense for more beds and staff to be in Auckland, given that was where a large number of prisoners came from.
