Grace Millane was last seen on Saturday evening in central Auckland.
Detective Inspector Scott Beard said her father was on his way to New Zealand and the rest of her family were understandably "distraught".
The distressed family released a plea on social media after Ms Millane had been missing for five days.
Beard said there was no evidence of foul play at this stage and police were speaking with people at the backpackers Millane was staying at - including those she was with on Saturday night.
Grace Millane's other brother, Michael Millane, said she had travelled to South America with an organised group, before arriving in New Zealand two weeks ago.
New details have emerged about the background of a missing British backpacker and her time in New Zealand.
Grace's father will fly to New Zealand, Michael said.
Grace is described as a European woman with brown hair and brown eyes.
She maintained regular contact with her family and friends, but vanished from a "party hostel" the day before her birthday.
The radio silence was "unusual" for Grace, Declan Millane said.
The investigation so far had concentrated around Millane's movements since she arrived in New Zealand, he said.
Her family in the United Kingdom raised the alarm on Monday and Detective Inspector Scott Beard said her disappearance was "out of character".
Her older brother said it was completely out of character for her not to be in contact with her family.
However she was travelling alone when she came to New Zealand about two weeks ago.
"I'm sure he'll want to know, first hand, what the police are doing to try to find his daughter", Beard said.
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". It has been shared thousands of times around the country.
Various sightings of Millane have her last wearing a black top, blue jeans and red sneakers.
Base Backpackers declined to comment to the Herald on Wednesday.
"She hasn't really replied to any messages between the family and it was her birthday on Sunday and she didn't respond to any messages".