The 22-year-old was last seen on Saturday night in the New Zealand city, where she had been staying in a hostel.
Auckland Police say he will remain in police custody until Monday morning when he will appear in the Auckland District Court.
'The police investigation today has concentrated on her movements and activities in Auckland since she's arrived in New Zealand, ' said Det Insp Scott Beard.
Police say she was last seen with a man, and they are now searching an apartment in the city.
Millane arrived in New Zealand on 20 November as part of a year-long trip.
In a tearful press conference on Friday Ms Millane's father, who has travelled to Auckland, said the "fun-loving" graduate's family are "extremely concerned" for her welfare.
Tonight's statement said the Millane family have requested privacy at this time and will not be making any further statements at this stage.
"Sadly the evidence we have gathered to this point of the inquiry has established that this is a homicide". 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.
Grace Millane, who was travelling the world after finishing university, went missing a week ago.
Her brother, Michael Millane, said the family began getting anxious on Monday when she didn't reply to messages. "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. we are all extremely upset and it is very hard at this time to fully describe the range of emotions we are all going through".
"We are all extremely upset and it is very hard at this time to describe the wave of emotions we are going through", he said.
Millane urged anybody who had seen or spoken to his daughter over the past week to contact police.
"Several of her belongings, including her passport are missing and police believe it is likely Grace has these items with her".
The family has set up a Facebook page - Help Find Grace. 'A large part of that focus has been around CCTV footage around Auckland'. "She has not returned to her hostel room in Auckland, New Zealand, and family members have had no contact since Saturday 1st December".
'Police have identified this man and he has been spoken to'.
Meanwhile, the scene examination at the Citylife hotel is continuing as detectives review hundreds of hours of CCTV footage.