The couple, who ran a gas station in the northern city of Rotorua, applied to Westpac Bank for a NZ$10,000 ($6,000) overdraft and had 1000 times that amount paid into their account. The two then withdrew some of the money and disappeared, Detective Senior Sgt. David Harvey said.
Harvey said Interpol has been contacted for help, suggesting authorities believe they may have fled abroad with the cash.
"We are currently conducting an investigation into the individuals that may have been involved in the withdrawal of that money," Harvey said.
Westpac Bank said in a statement it was "pursing vigorous criminal and civil action to recover the sum of money stolen," but declined further comment.
Massey University banking lecturer Claire Matthews said the "lucky" recipients likely would not get away with the cash.
"They've effectively, I guess, become thieves - but it is only going to be a matter of time" before they are found, she told the NewstalkZB radio network.
The pair would be hard pressed to argue they honestly believed they were entitled to such a huge sum of money, she added.
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