Police say they are questioning a 26-year-old man who was seen with her on the night of her disappearance.
Auckland City Police Detective Inspector Scott Beard told a press conference: "The evidence we have located so far, our scene examination, some of the CCTV footage we have, and our investigation, has determined that Grace is no longer alive and that this is a murder investigation".
He said: 'Just after 3pm this afternoon (Saturday) a 26-year-old man was located at a central Auckland address by police.
Grace Millane's father David said his daughter had been excited about coming to New Zealand and had bombarded the family with images of her adventures since arriving.
This afternoon police said they had assessed Millane's property left at the backpackers where she was staying - and found some items missing.
He added the "thoughts of all New Zealanders will be with Grace's family tonight".
The Essex woman had embarked on a year-long worldwide trip following her university graduation.
News of the murder inquiry comes hours after Millane's family said they were "staying very positive" as the search for her continued.
"We still do not know where Grace is".
"All I can say is that we know they were together from the time at the Sky City Hotel".
After visiting Peru, she arrived in New Zealand on November 20 and had been in near-daily contact with her family until December 1 - the day before her 22nd birthday.
In a statement released on Saturday morning (New Zealand time), they said it had been "an extremely hard and emotional time for us all".
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'He was brought back to the Auckland Central Police Station and is now speaking to us in relation to the murder of Grace Millane.
Members of Millane's family have made appeals on Facebook for information.
He said: "As part of our investigation, we have reviewed hours and hours of CCTV footage and this will continue throughout the weekend".
Beard said "that property is going to be somewhere, the clothing is going to be somewhere, we haven't found it".
Police want the public to help find this necklace belonging to backpacker Grace Millane.
DI Beard confirmed that the man being questioned by police on Saturday was the same individual.
In the statement issued on Saturday, Millane's family praised Auckland police "who have been outstanding in their support and efforts in helping to find Grace".
"Grace is a lovely, outgoing, fun-loving, family-orientated daughter".
"Her family are devastated", he said.
"Our hearts go out to them".
"At this point our enquiries have not led us to any further confirmed sightings of Grace, and the last known sighting is of her entering the Citylife Hotel", he said.
Anyone with information about the missing items has been advised to contact 0800 676 255.