Gunfire erupted just before 4 p.m. outside the Evergreen Recreation Center in the 2800 block of E. 2nd Street, near First Street Elementary School.
Bystander video showed grieving family being held back by officers as they tried desperately to get to their son, whose body was covered in tarp as police investigated.
One person, who has not yet been identified, is in custody and a weapon has been recovered, according to police.
No motive for the shooting has been determined.
"Obviously, it's very preliminary. I don't know if they knew each other. I don't know if there was an argument, but there was some sort of discussion and then the shooting," said LAPD Capt. German Hurtado.
After the shooting, police set up a perimeter as a search continued for another suspect.
The name and age of the victim were not immediately released.
The shooting is the second in which a juvenile was fatally shot near a Los Angeles-area elementary school within 24 hours. On Monday, a 12-year-old boy was killed when two suspects approached the vehicle he was in and opened fire near Wilmington Park Elementary School. That shooting also wounded an adult woman and a 9-year-old girl.
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