WELLINGTON, New Zealand — A man in Auckland, New Zealand, will be charged with the murder of a British backpacker who was last seen entering a hotel a week ago, the day before her 22nd birthday, the police in New Zealand said Saturday.

Detective Inspector Scott Beard said officers had not found the body of the victim, Grace Millane, but had concluded that she had been killed.

A 26-year-old man, whose name was not released, will appear in the Auckland District Court on a murder charge on Monday.

Inspector Beard said Ms. Millane was last seen on the night of Dec. 1, entering the CityLife Hotel in downtown Auckland with a man. The inspector told reporters that closed-circuit television footage showed the two had spent time together at “a number of places” earlier that evening.

Ms. Millane’s family in England became worried when she did not contact them the following day. After arriving in New Zealand on Friday, her father, David Millane, said his daughter had “never been out of contact for this amount of time” and had “bombarded” the family with pictures and stories from her trip. British media reports described Mr. Millane as a millionaire property developer.

The police in Auckland began investigating Ms. Millane’s disappearance on Wednesday, after her family reported her missing. Family members posted on social media during the week, appealing to the public for information.

“It was her birthday on Sunday but we hadn’t heard from her,” Michael Millane, the victim’s brother, told Sky News. “One of us would usually have a chat or a text every day.”

Ms. Millane, from Wickford, in Essex, had planned to spend a year traveling the world following her graduation in September from the University of Lincoln. After a six-week tour of Peru, she arrived in New Zealand alone on Nov. 20, planning a two-week stay before traveling to Australia.

She had been staying at a hostel in Auckland, New Zealand’s largest city. Both the hostel and the hotel where she was last seen are in a busy downtown area.

On Friday, the police first said they had spoken to a man in relation to her disappearance. Inspector Beard said on Saturday that officers had found a vehicle of interest and were investigating where it had been.

He said that an examination of the vehicle and of a room at the hotel where Ms. Millane was last seen had led officers to conclude that she was dead.

“We still do not know where Grace is,” Inspector Beard said. “We are determined to find her and return her to her family.”

New Zealand’s annual murder rate is in the double figures, and deadly attacks by strangers are rare.

In 2008, Karen Aim, a 27-year-old tourist from Scotland, was killed in the city of Taupo by a local teenager. And in 2005, Birgit Brauer, 28, was found dead in a national park near the city of New Plymouth. She was killed by a man who picked her up while she was hitchhiking.