It comes as the military faces concerns over the presence, both current and historic, of personnel holding extremist views.
It was removed on Tuesday, five days after it was published following an internal backlash and replaced with a statement from Army Chief Major General John Boswell, who apologised and accepted the decision to award the piece first place was an error.
He said out of the two entries, the essay won because it was "well-written", but the views were not compatible with the army's values.
"I made this decision when it became clear that publishing it was being seen as endorsement of the views contained within it, which could not be further from the truth."
It was important to seek to understand where other views existed, but in this case publishing the essay was viewed as "undermining both the inclusive culture we are seeking and the work that is being done across all ranks to effect this change".
"Work that is incredibly important, not just to me, but to our organisation."
After questioning from Newstalk ZB, Defence Minister Peeni Henare said he delivered a blunt message to Defence Force chief Air Marshal Kevin Short yesterday.
He told Short his expectations were that "we're better than that, and have values that don't align with the essay."
"Ultimately, the decision to either put it up or take it down sits with the Army."
Henare said he first heard about the essay on Tuesday, once it was posted online.
By Wednesday afternoon, Henare hadn't read it, but said he was satisfied with the outcome.
"Of course, it isn't measured on how we react to this particular incident. It's what we do to make sure in the future, this doesn't happen again."
Henare was "unsure" if he spoke with Short before or after the essay was taken down.
National said it was "really strange" the essay had been scrubbed from the internet.
The party's Defence spokesman Chris Penk said it was concerning if it had been removed because it didn't fit a pre-determined narrative.
"If you run an essay competition and pick a winner based on merit, then there should be no good reason that essay mysteriously disappears."
Act Party leader David Seymour said although he didn't think the essay would "win a Pulitzer prize", he said the army needed a culture of healthy debate.
"The New Zealand Army used to fight for free speech, now it's fighting against it."