The first teenager has been bailed after admitting possessing a machete as disorder broke out at the Intu Bromley centre. Shoppers panicked after rumours of a gunman.
Armed police were called at about 15:45 GMT and found a boy with a head injury. Two knives were recovered.
Both boys have also been charged with common assault and violent disorder.
A second 16-year-old boy has been charged over an alleged knife fight at a London shopping centre on Boxing Day.