The fire happened around 6:09 p.m. Monday in Brookhaven Park.
Firefighters quickly responded and put out the flames, police said, but the fire caused structural damage to the playground equipment.
Photos released by New Castle County police show portions of the melted playground.
Anyone with information is asked to contact Fire Marshal Thomas Looney at (302) 323-5375 or via email at Thomas.Looney@delaware.gov or Crime Stoppers at (800) TIP-3333.