Authorities said the dog, called Grizz, could not be captured after it ran off. The incident grounded 16 flights and caused delays for several hours.
An airport official said the decision to shoot the dog was a last resort.
But it has been met with outrage, with many asking why the dog could not have been tranquilised instead.
Grizz was a 10-month-old trainee sniffer dog at Auckland Airport handled by the government's Aviation Security Service (Avsec).
Avsec spokesman Mike Richards said that around 0430 local time (1530 GMT Thursday) Grizz was getting into a dog unit wagon parked in the airport's public landside area, when "something" caused it to escape.
At that point a gate connected to airside, or security area, had been opened to let a truck through. Grizz managed to run through the gate onto the tarmac.
'Exhausted every option'
Mr Richards said a "massive effort" was launched to locate the dog in pitch black conditions, and for the first two hours Grizz could not be found.
When it was finally located, "he would not let anyone near him and kept sprinting across runways.
"We tried everything: food, toys, other dogs, but nothing would work," said Mr Richards, adding that the area was "too vast and too open" to erect temporary fencing.
Airport officials finally ordered police to shoot Grizz.
"We exhausted every option available and could not catch it," an Auckland Airport spokesman told the BBC.
When asked why the dog could not be tranquilised, the spokesman said: "I do not have the answer to that. But there were no tranquiliser guns at the airport, and the police do not have them either."
She said tranquilisation would be part of an incident review undertaken by Avsec.
New Zealand animal rights organisation Safe said it was "appalled about the needless killing of this dog".
"A tranquilliser gun should have been used after efforts to catch the dog failed. If such a gun was not available - which it should - then they could have borrowed one from Auckland Zoo or elsewhere," a spokesman was quoted as saying by the New Zealand Herald.
The incident has prompted a deluge of angry comments on the airport's Facebook page.