"Grace has been missing for 5 days", her brother Michael Millane posted on Facebook on Tuesday.
Her social media accounts had also not been updated.
Police confirmed a missing person's report was filed today for Millane.
'We are really, really anxious and concerned about Grace.
The father of a British tourist missing in Auckland is flying to New Zealand in a bid to find her.
Grace had two mobile phones with her but they go straight to voicemail if people ring, her brother said.
Police are appealing for anyone who may have seen Grace on Saturday night or may have information on her whereabouts to contact Police on (09) 302 6970.
Mr Beard said none of her roommates at the backpackers were with her on Saturday evening and there was sufficient evidence to suggest she was going to go back to the hostel to collect the items she had there.
"If she gets this message, we would urge her to get in touch with us as soon as possible so we know she's OK".
The witness said the young woman, who she believes to have been Millane, did not have her arm out with her thumb stuck up in the air like a hitchhiker.
She has not returned to her Auckland hostel in several days.
Her birthday was on Sunday and police said it was unusual for her not to contact her family then.
He added that she had travelled to Peru as part of an organised group for six weeks but had not travelled on her own until she arrived in New Zealand two weeks ago.
"Being out of contact with family for this long is especially out of character for her".
New details have emerged about the background of a missing British backpacker and her time in New Zealand.
While she was travelling alone, Michael Millane said she had made a lot of friends.
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".
"We are unable to make further comment while police are investigating the matter".
Various sightings of Millane have her last wearing a black top, blue jeans and red sneakers.
It is the last time anyone has seen Millane, whose 22nd birthday was the next day.