Kaino, who has won two Rugby World Cups, had not been named in the matchday squad with Liam Squire given the starting blindside flanker role.
NZR said a media report in Australia about his personal life had necessitated the 34-year-old's return to Auckland.
The world champions have been enshrouded in off-the-field controversies this week, with NZR re-opening an investigation into scrumhalf Aaron Smith's tryst with a woman, who was not his partner, in a toilet at Christchurch Airport last year.
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NZR chief executive Steve Tew said on Saturday the week had meant his organisation were under pressure.
"We certainly understand that our game and our players are under public scrutiny and these latest stories are concerning," Tew said in a statement. "As an employer, we will take some time to assess this.
"While NZR does not wish to comment on individual behaviour, it is clear that this is really hurting rugby, all the people concerned, our fans and supporters.
"We take these issues very seriously, and are also mindful that these issues affect people with families and loved ones."
The behaviour of their players has not been the only thing distracting the team in Sydney ahead of the match, which doubles as the first of three Bledisloe Cup tests.
A trial against the team's Australian security contractor also ended on Friday with Adrian Gard found not guilty of public mischief after a listening device was discovered in the team's hotel ahead of the same fixture last year.
NZR were criticised last year for their handling of an investigation into the Waikato Chiefs' 'Mad Monday' celebration where the team hired an exotic dancer, who said she was touched inappropriately and had alcohol thrown at her.
The incident forced NZR to conduct a review of its culture and treatment of women. Tew said the review was expected to be made public next month.
"At a time when we are grappling with our cultural reputation, the respect and responsibility review, which is currently under way, is even more important," Tew said.
"The review is being presented to the NZR Board this month and we are looking to make that public sometime in September."
(Reporting by Greg Stutchbury in Wellington; Editing by Sudipto Ganguly)
