Petra Srncova, 32, who lives in the Camberwell area, was reported missing on Friday, 3 December by a concerned work colleague.
Petra was last seen at 7.45pm on Sunday, 28 November. She is believed to have been wearing a green coat and carrying a red backpack.
Police have contacted her family in her native Czech Republic and they also have not heard from her.
Police are growing increasingly concerned for Petra’s welfare and are asking anyone who has seen her, or has information as to her whereabouts, to make contact immediately.
Detective Superintendent Clair Kelland, from the Central South Command Unit which covers the area that Petra lives in, said: “Petra’s disappearance is out of character and, of course, her family and friends are very worried.
“We are also growing increasingly concerned for Petra’s welfare and have officers working hard to try and find her.
“If you have any information whatsoever, please get in touch and help us with our enquiries.”
A man, no further details, has been arrested in connection with her disappearance and taken into custody, where he remains.
Anyone with information is asked to call 101 or tweet @MetCC referencing 21MIS037753.