Flatley, who was a late withdrawal from last Saturday's Test against the South Africa in Perth with blurred vision, has not fully recovered and will be given as much time as possible to return to full health.
His absence is another blow to the Wallabies, who must beat New Zealand to avoid their fifth straight Test loss.
Wallabies team doctor Martin Raftery revealed Flatley has had further tests on the injury this week, as well as being reviewed by a specialist.
"It's been well documented that Elton has had problems with concussion this year and we've had to monitor that closely through the Super 12 and Test season," Raftery said.
"Investigations suggest the blurred vision is related to prior concussive episodes and the best thing for Elton is to have the opportunity to recover fully and this means a period away from contact training.
"Elton has already seen a specialist in Melbourne earlier this year, as well as a doctor in Brisbane, and an eye specialist this week.
"He will continue to seek the best advice available and needs time to fully recover before we can evaluate him further."
Wallaby coach Eddie Jones admits while it's disappointing for Flatley, it's important he does what is right for him and his career in the long term.
"Our main concern has always been for Elton's health, and the advice suggests he needs to take a break from the game at the moment," Jones said.
"We don't know how long a break that is, but at this stage it is highly unlikely he would be available for selection for the spring tour, and the earliest we would see him back is for the Reds in the Super 14 next year."
The 27-man Wallaby squad flew to Coffs Harbour on Friday to continue preparations for the Auckland Test.