Police are appealing for witnesses and information after an incident in Burgess Park and Tesco in Old Kent Road on Tuesday night.
Police were called just before 6pm on Tuesday to reports of up to 600 people taking part in a water fight in Burgess Park.
A Scotland Yard spokesman said that this escalated over the next hour to reports of a large disturbance in the park that spilled out into the nearby streets, with a crowd totalling between 1,000 and 1,500 people.
Two 16-year-old boys were stabbed at the event. Neither suffered life-threatening injuries and one remains in hospital.
Just after 8pm officers were called to Tesco in Old Kent Road to reports of a group of up to 200 people causing damage inside the store and stealing items.
Two female customers suffered minor injuries but declined medical assistance.
Police say that the crowd was dispersed by 11pm. There were no arrests.
"While at this stage we do not believe the events at Burgess Park to be linked to disorder elsewhere in London last night, clearly there are similarities with incidents quickly breaking out amongst a large group of youths," said Detective Chief Superintendent Simon Messinger, Southwark's borough commander.
"Two boys were stabbed, fortunately neither suffering serious injuries, and a supermarket was also ransacked which was terrifying for staff and customers alike.
"These are serious incidents and unacceptable. We are appealing for any witnesses or anyone with information to come forward."
Anyone who can help is asked to contact police via 101 or Crimestoppers anonymously on 0800 555 111.