It said the army understood there had been other incidences of flu outbreaks within New Zealand.
"We wish to act responsibly to reduce any impact on the wider health system," the post said.
Soldiers are receiving medical support and measures were being implemented throughout the camp to ensure the virus was contained.
The army said the graduation delay would ensure soldiers were fit and able to take on their next challenge.
"We understand families and friends will be disappointed, and we sorry that more notice could not be given due to the swiftness of the symptoms and spread of the virus," it said.
"However we are sure the reasons why this decision has been made will be understood."
The army has apologised for the inconvenience its decision had caused but said it remained confident that "people will agree that the health and safety of our service members and their families is paramount".
A surveillance report released by ESR on Wednesday showed there had been a significant increase in influenza-like illness in the week to June 16 across New Zealand.
Hospitalisation rates for influenza-positive respiratory infection cases, although decreasing, was still about six times higher than normal for this time of year.