Police gave out a description of the young woman, as well as details about the last confirmed sighting of her.
"Grace is a 22-year-old European woman with brown hair and brown eyes. She is approximately 5ft 6in (168cm) in height and 58kg.
"At this stage, Grace was last sighted around 7pm on Saturday, 1 December, on Victoria Street, Auckland CBD.''
Detective Inspector Scott Beard said officers had spent the past 24 hours trying to piece together her last known movements, who she has associated with and the circumstances of her disappearance.
Various sightings of Millane have her last wearing a black top, blue jeans and red sneakers. Others have her in a black dress and white shoes.
Beard said anyone who believes they may have seen Millane on Saturday night or has information about her whereabouts is urged to contact police immediately.
An Auckland woman believes she saw missing woman near the Southern Motorway in Manukau.
The witness, who asked not to be named, told the Herald she believed she saw her standing by the Manukau on-ramp.
"Where she was standing, it was really bizarre and she was by herself, nobody around just a girl on her own," she said.
"I can honestly 100 per cent say I saw a young girl, absolutely so close to her description that it's not funny, and there was no way I was going to stop.
"She was in a very unusual place to stand, I would have thought a hitchhiker would have stopped on the left-hand side to get in the car, she was on the other side."
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 could not remember if the young woman had bags with her or not or whether she saw the woman standing by the road on Friday or Monday afternoon.
"I looked at the photo [of Millane] and I was quite adamant I had seen that girl," she said.
"I just saw a young girl and I thought she had like a raincoat ... she had a bigger sort of jacket, not a fashion like one."
Millane's family sparked the investigation into her disappearance yesterday after they became alarmed when she didn't respond to birthday messages on Sunday.