Julia Skala left her home in Mitcham around 1pm on January 8 and has not been seen or heard from since.
Police say she left her mobile phone behind, and is not believed to have had any money with her when she disappeared.
Her mother reported her missing the following morning, on January 9. Scotland Yard immediately launched an investigation but she has not been found.
In a statement issued on Wednesday, the teenager's "extremely worried" family said: “Julia, you are loved and missed terribly.
"No matter what the reason was for you to leave, you aren’t in any kind of trouble and we just want to know you are safe.
"Please, just let someone know you are OK.”
At the time of her disappearance, Julia was wearing a black North Face jacket, black trousers and white Nike trainers. She was also carrying a black Nike rucksack.
Scotland Yard detectives have spent nine days searching for Julia, including scanning CCTV footage and carrying out house-to-house enquiries.
Detective Chief Superintendent Clair Kelland, in charge of policing for Merton, said officers "have been working around the clock to try and find her".
"We have gathered and examined hours of CCTV and doorbell footage, spoken to many people who know her and carried out enquiries with those who live in the area to establish whether they have any information that might help our investigation," she said.
“Julia has never been away from home for this long and obviously her family are extremely worried.
“While there is no evidence to suggest she has come to harm, we are growing increasingly concerned about her welfare.
"She did not take her mobile phone with her and there has been no activity on social media or known contact with her friends.
“We also do not believe she had a credit or travel card, or any cash when she left the house.”
Julia lives in Mitcham, but also has links to Lambeth, Camden and Islington and the Met Police says it is possible she has travelled to these places using public transport.
Anyone with information should call police immediately on 999 quoting the reference 24MIS000879. Share non-urgent information by calling 101.
You can also contact the Missing Person's charity anonymously on 116 000.