Thi Khanh Ly Duong, aged 17, was reported missing by staff at her boarding school in Staffordshire on May 1.
Thi, also known as Ly, is from Vietnam but her guardians live in Handsworth.
Officers from West Midlands Police say they believe Thi left Asda on Avon Road, Cannock, just before 6.30pm on Saturday afternoon and was picked up by a taxi outside the store at around 6.45pm.
She was later dropped off in Holly Road, near to Grove Lane in Handsworth, but has not been seen or heard from since.
She is described as being around 5ft in height, with a slim figure and long, black hair. She was last seen wearing light jeans and a light-coloured hoody, with a black jacket over the top, Nike flip-flops and a large black handbag.
A spokesman for West Midlands Police said: "We're urgently appealing to trace a teenager who has gone missing in Handsworth. Have you seen her?
"If you have any information about where she might be, please contact us as soon as possible via live chat at www.west-midlands.police.uk 8am – midnight, or call 101 anytime.
"If seen, please call us on 999. Thank you."