The teen was detained on suspicion of riotous behaviour after police came under attack when they responded to a report of the park in the Stewart Street in the Market area being damaged.
The flooring of the soft area had been set on fire and fire crews who attended also were attacked by youths, police said.
A PSNI spokesperson said: “Police will be maintaining a presence in the area and we would appeal to any young people to think twice before getting involved in this sort of antisocial behaviour.
“It can have serious implications for your future and damaging Police or Fire Service equipment can have grave consequences for those who need our help.”
The boy remains in police custody at Musgrave PSNI station.