Agnes Akom, 20, from Cricklewood went missing on Sunday, May 9, after leaving home.
A 63 year-old man, who is believed to have been known to her, was arrested in North Acton on Monday on suspicion of murder and false imprisonment.
He was taken into custody and is being questioned at a north London police station.
Ms Akom, also known as Dora, is a Hungarian national who has been living in the UK for five years.
Detectives from the Met’s Specialist Crime Command continue to appeal to the public for any information relating to Agnes’ whereabouts, as extensive searches to locate her continue.
She is described as approximately 5ft 5ins tall, blonde-haired, and is believed to have been wearing a distinctive white faux-fur coat blue ripped jeans and light pink trainers on the day she first went missing.
Detective Chief Inspector Neil John, leading the investigation, said: “Our officers are working tirelessly to locate Agnes, who has now not been seen or heard from in 10 days. There are serious concerns for Agnes’ safety and it is our priority to find her as soon as possible.
“We are conducting extensive searches in the Park Royal and Holland Park areas today following last night’s arrest, and are continuing to utilise all investigative opportunities to build a clear picture of her movements.
“We are following every lead possible and are appealing for the public to help us in our work. If you may have seen Agnes, or have any information on her whereabouts over the past 10 days, please contact police.
Anyone with information is asked to call police on 101 or Tweet @MetCC quoting 21MIS013067. The incident room can also be contacted direct on 0208 3580 100.