Homicide investigators say 18-year-old Amir Jamal fired the shots that killed 30-year-old Nyeme Taylor on Sunday.
Police say Taylor was intervening in a fight involving his son when he was shot six times.
Investigators say Taylor had brought his son to the rec center's playground following an earlier confrontation involving the boy. Police Taylor was shot during and ensuing confrontation.
Taylor's 15-year-old daughter was wounded in the leg and two girls, ages 10 and 6, were also shot.
The shooting happened during an unauthorized party that attracted 150 or more to the rec center.
Jamal was arrested Thursday. It was not clear if he had an attorney.