British backpacker's disappearance in New Zealand being treated as suspected murder
They had previously been speaking with him over the disappearance.
Det Insp Scott Beard said the evidence told them she was "no longer alive".
The 22-year-old, from Essex, described by her father as "lovely" and "family-orientated", vanished in New Zealand a week ago.
Members of Millane's family have made appeals on Facebook for information.
Police later said they had spoken to the man and that he was a "person of interest", although he was not held in custody. He would not confirm what type of vehicle it was.
He added the "thoughts of all New Zealanders will be with Grace's family tonight".
The last confirmed sighting of Millane was at the CityLife Hotel, in Queen St, at 9.41pm on Saturday.
"Sadly the evidence we have gathered to this point in the inquiry has established that this is a homicide", he told a press conference. "This issue here is Grace is still missing and we want to find her".
Police said they are still looking for Ms Millane, 22, who was last seen in the city on December 1, although evidence suggested she had been killed.
DI Beard said the investigation into Grace's disappearance was "progressing rapidly".
"We don't know what's happened to the property of hers that has been missing", he said.
New Zealand police confirmed they are now treating British backpacker Grace Millane's (pictured) disappearance as a homicide.
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
"Several of her belongings, including her passport, are missing and police believe it is likely that Grace has these items with her".
In a statement released on Saturday morning (New Zealand time), they said it had been "an extremely hard and emotional time for us all".
Officers found the 26-year-old man at a central Auckland address at 3pm, and interviews were still taking place late this afternoon.
'He was brought back to the Auckland Central Police Station and is now speaking to us in relation to the murder of Grace Millane.
The much loved daughter and sister arrived in New Zealand on November 20, as part of a year-long, worldwide overseas experience that began earlier this year in South America.
She had daily contact with her loved ones via social media but her father, David Millane, said the family last heard from her on December 1.
Photos on her Instagram showed she travelled to Cape Reinga with friends before returning to Auckland. She was traveling alone when visiting New Zealand.
An emotional Beard said it had been a tough time for all involved in the investigation.
"Everybody who is a parent out there will understand what their family is going through".
Anyone with information about the missing items has been advised to contact 0800 676 255.
David Millane, the father of missing backpacker Grace Millane, says his daughter has "never been out of contact for this amount of time".