The blaze was first reported shortly before 1:20 p.m. in the 2400 block of E. Porter Street south of downtown L.A.
There were no immediate reports of any injuries.
Fire officials described the structure as a 14,000-square-foot recycling facility with baled paper goods.
There were 89 Los Angeles Fire Department personnel assigned to the blaze.
Crews appeared to get a quick handle on the fire. By 1:45 p.m., there was plenty of smoke but no visible flames on scene.
The cause of the fire was not known.