Police later said they had spoken to the man and that he was a "person of interest", although he was not held in custody.
Ms Millane was last seen last Saturday night entering the four-star CityLife Hotel at 9.41pm.
Auckland Police Detective Inspector Scott Beard said a 26-year-old man is being questioned in relation to Grace Millane's whereabouts.
Police investigating the murder of British tourist Grace Millane stand by a cordoned off crime scene along a section of Scenic Drive in the Waitakere
Detective Inspector Scott Beard made this known at a news conference in Auckland.
Prior to her dissapearance, Grace had been in contact with her family everyday and concerns were raised when she didn't respond to birthday messages on Sunday December 2.
"I know that the thoughts of all New Zealanders will be with Grace's family tonight and I want to reassure everyone both here and overseas, that NZ Police are determined to do everything we can to find Grace".
Police have identified and secured a vehicle of interest.
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New Zealand police confirmed on Saturday afternoon they are treating the investigation as a homicide.
A vehicle seized in relation to Millane's disappearance, meanwhile, appears to be the key piece of evidence in her death, a former police inspector says.
"At this stage we are not able to confirm whether Grace has been located at this site".
Police have also released photos of a necklace and pink Casio Baby-G watch Millane was thought to be wearing when she disappeared, and said her passport was also missing.
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On Friday, the tourist's father David Millane said his daughter was on a year-long backpacking experience across the world.
Police want the public to help find this necklace belonging to backpacker Grace Millane. Grace has never been out of contact for this amount of time and is usually in daily contact with either her mother, myself or her two brothers.
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