The incident happened at the Blackheath Easter funfair in Prince Charles Road just before 3.50pm yesterday (April 8).
Officers and London Ambulance Service crews attended and treated one person for minor injuries.
It is unknown how they sustained their injuries, however, they were discharged at the scene shortly after.
Police believe that the majority of those involved had already left the scene before their arrival.
There have been several arrests for separate offences, but that the exact arrest figure is unknown at this stage.
Officers arrested multiple people, including on suspicion of possessing an offensive weapon in a public place.
A section 60 order was authorised for the area allowing officers to conduct stop and searches on individuals without reasonable suspicion in a defined area and time.
Police enquiries are ongoing.
A spokesperson for London Ambulance Service said: “We were called at 3.48pm yesterday (8 April) to reports of an incident in Prince Charles Road, Blackheath.
“We sent resources to the scene including ambulance crews, incident response officers and members of our Tactical Response Unit.
“We responded alongside colleagues from the Metropolitan Police Service and London Fire Brigade.
“We treated one person for minor injuries and discharged them at the scene.”
A Met spokesperson said: “On Tuesday, 8 April police were made aware of large group of youths causing disorder on Blackheath Common.
“Officers are currently on scene dispersing youths who may still remain, while the majority were cleared throughout the afternoon.
“There were several arrests for separate offences, including arrests for possession of an offensive weapon in a public place.
READ MORE: Pictures show huge police presence after incident near Blackheath funfair
“A section 60 order has been put in place within the area.
“Police continue to monitor the situation.
“Enquiries are on-going.”
