The shop, which began in Brixton for 15 years and blossomed into a successful chain of stores is looking for a new site in the area but has yet to find one.
The lease has expired because the premises will form part of the entrance of a £4.5million Holiday Inn in the former Woolworths site.
Creative directo Maureen O’Biren said: “Brixton was my first store and definitely my favourite. We opened in 1999, before you could get a decent coffee – how time flies!”
She added: “I can’t thank our Brixton customers enough for their support, humour and energy over the years. Joy wouldn’t be Joy if we had opened anywhere else.”
As a final thank you to its customers, Joy will be holding a sale event in the run up to the closing date.