Her father, David Millane, said they last had contact on the day she vanished. The murder suspect, a 26-year old man, is scheduled to appear at Auckland district court on Monday, The Guardian reports.
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".
David Millane arrived in New Zealand on Friday morning, after the family raised the alert earlier in the week, having not heard from Grace since Saturday (December 1) - which he said was unusual.
A British backpacker missing in New Zealand since last weekend was murdered, police said.
There was no evidence they knew each other before Millane disappeared but Detective Inspector Scott Beard wouldn't comment on speculation they may have met on Tinder.
He also added that Millane's current whereabouts remain unknown, and that the police are "determined to find her and return her to her family".
Back home in Essex, church services will be held to remember Millane.
The backpacker's birthday was on Sunday, but she did not contact her family.
Officers established the man was with Millane on Saturday, December 1, and that they went to a number of locations before going to the City Life Hotel. "Somebody may find it somewhere, we don't know what has happened to it". "They're shocked and saddened by what's happened".
Police said she was seen the same day leaving an Auckland hotel with a "male companion".
Auckland City Police Detective Inspector Scott Beard said on Saturday: "Just after 3pm this afternoon (2am GMT) a 26-year-old man was located at a central Auckland address by police, he was brought back here to the Auckland Central Police Station and is now speaking to us in relation to the murder of Grace Millane".
Bell said the police would be doing "forensic examinations at length" on the auto, trying to find any physical evidence - DNA, fingerprints, or clothing fibres.
Police say Grace Millane was last spotted entering CityLife hotel in Auckland's CBD with a man on Saturday.
Another priority would be finding three items which police said were missing - Millane's passport, a pink Casio Baby-G watch and a necklace.
Beard said "that property is going to be somewhere, the clothing is going to be somewhere, we haven't found it. Somebody may find it somewhere, we don't know what has happened to it", Beard said.
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.