The 16-year-old boy was arrested at his home in the borough of Lewisham on suspicion of affray at intu Bromley.
He was treated in hospital for a minor wound before being taken into custody.
A second 16-year-old boy arrested at the scene on Saturday on suspicion of affray and possession of a weapon remains in custody.
Scotland Yard originally said the first person arrested had suffered a minor head injury during the incident and "was believed to be in his 20s".
The force later issued another statement putting his age at 16.
"At this stage officers believe he sustained the injury as a result of an altercation between a number of youths," it added.
Police, who were called at 15:45 GMT on Saturday to reports of an injured youth, say they recovered two knives.
A photograph taken by a member of the public appeared to show that a machete had been found.
Video filmed at the scene also appeared to show shoppers fleeing in panic.
A second teenager has been arrested after a suspected knife fight broke out at a London shopping centre on Boxing Day, the Metropolitan Police has said.