The 26-year-old being questioned is the person of interest police mentioned yesterday.
'Sadly the evidence we have gathered to this point of the inquiry has established that this is a homicide.
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.
They said that several of Ms Millane's possessions, including her passport, were missing.
Grace Millane was last seen at the city center of Auckland around 7 pm December 1.
Police want the public to help find this necklace belonging to backpacker Grace Millane.
"Her family are devastated", he said.
Dozens of calls had been made to the 0800 investigation helpline number, and that information continued to be reviewed and assessed, Beard said.
Ms Millane, from Essex, was described as a "lovely, outgoing, fun-loving, family-orientated daughter" by her father, David Millane.
Ms Millane was in New Zealand on a gap year, having arrived in the country on November 20.
Asked if the pair had met on the Tinder dating app, the detective said: "I'm not going to speculate on how they met".
Detective Inspector Scott Beard said a scene examination at the hotel is continuing and investigators were progressing with the viewing of hundreds of hours of CCTV footage.
They revealed yesterday that their investigations included questioning the man who was with Millane when she was last seen.
Earlier on Saturday police released images of her necklace and watch and urged anyone who recognised the items to come forward.
A British backpacker missing in New Zealand since last weekend was murdered, police said.
She had booked to stay at the Base Backpackers hostel in central Auckland until 8 December.
'We're all extremely upset and it's very hard at this time to describe the range of emotions we are going through'. 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.
A spokesman for the Foreign Office said: "We are providing consular support to the family in the United Kingdom, and working with the New Zealand Police in relation to reports of a missing British national in New Zealand".
Beard wouldn't say whether police had seen footage of the man leaving CityLife Hotel or if he thought Millane was killed in the hotel, a large apartment-style complex.