The plane landed safely around noon after dumping its fuel, which fell onto Park Avenue Elementary School, located about 16 miles (25 kilometers) east of the airport.
The Los Angeles Fire Department said 17 children and nine adults complaining of skin irritation were treated on the spot and did not require hospitalization.
In a statement to AFP, a Delta spokesperson said the fuel was released to allow the plane to land safely.
"Shortly after takeoff, Flight 89 from LAX to Shanghai experienced an engine issue requiring the aircraft to return to LAX," the statement said. "The aircraft landed safely after an emergency fuel release to reduce landing weight."
The fuel also landed on another school in south Los Angeles but there were no injuries among students or staff, authorities said.
In a statement, the Los Angeles Unified School District said students and staff were on the playground of the elementary school when the incident happened.
They "may have been sprayed by fuel or inhaled fumes," it said, adding that school officials "immediately called paramedics, who are on the scene and are treating anyone who is complaining of skin irritation or breathing problems."
The Federal Aviation Administration said it is investigating the incident and said there are special fuel-dumping procedures for aircraft operating into and out of major US airports.
"These procedures call for fuel to be dumped over designated unpopulated areas, typically at higher altitudes so the fuel atomizes and disperses before it reaches the ground," the agency said in a statement.