Ms Millane left the United Kingdom six weeks ago to travel the world after finishing university.
Ms Millane, an advertising and marketing graduate who graduated from the University of Lincoln a year ago, had spent six weeks travelling with an organised group in South America before going to New Zealand alone.
'We are really, really anxious and concerned about Grace.
Detective Inspector Scott Beard this afternoon said her disappearance was "out of character", after her family in the United Kingdom raised the alarm on Monday.
She has not returned to her hostel room in Auckland New Zealand, ' her older brother Michael Millane wrote on Facebook.
"We last had contact with her on Thursday, but it had been daily before that", he said.
He told Checkpoint Ms Millane has been in New Zealand since late November and was last seen at 7pm on Saturday night at Sky City on Victoria Street in Auckland's CBD.
It was her first time travelling solo.
Grace's father is due to arrive in New Zealand on Friday, reports Stuff.
Another brother urged people to share the post, adding: "We haven't heard from my sister since Saturday".
"Grace is a 22-year-old European woman with brown hair and brown eyes".
"We are working with the family in the United Kingdom and New Zealand police in relation to reports of a missing British national in New Zealand". She's approximately 5ft 6in (168cm) in height, and 58kg.
Tony McLeod, consular manager at the British High Commission in Wellington, said the commission were providing consular assistance to the family back in the UK.
Det Insp Scott Beard, of Auckland City Police, said more than 20 staff were working on the case.
Various sightings have her wearing either black top, blues jeans and red sneakers, or a black dress with white shoes.
"There have been a few tips and we will be working through them".
"There's been nothing (communication since Saturday) between her and her family, no", Mr Beard said.
Base Backpackers declined to comment.
"This is particularly out of character, especially as it was her 22nd birthday on Sunday".
"We are working with the family in the United Kingdom and New Zealand Police in relation to reports of a missing British national in New Zealand", he said.
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