The blaze was reported around 3:15 p.m. at American Chemical & Sanitary near Jefferson Street and Miraloma Avenue.
Firefighters said the five-alarm blaze initially engulfed the building, where spot fires continued to pop up late into the evening.
"We fought the fire for several hours. There's still active flames going on inside the building now," said police Sgt. Daron Wyatt, an Anaheim public safety spokesman. "There are trailers literally stacked wall-to-wall with toilet paper and paper towels.
"They're very tightly packed," Wyatt added, "so once we pull a layer out, the layer behind ignites."
At first it was unclear what sort of chemicals were in the 30,000-square-foot building, but a hazmat team determined nothing toxic was burning in the incident.
One business employee suffered a minor leg injury, Anaheim Fire officials said. Two firefighters were also transported to a hospital for treatment after suffering electric shock and heat exhaustion, respectively.
Both firefighters were later released and returned to the scene to continue working, Wyatt said.
Anaheim Fire said evacuations were limited to the surrounding area.
The cause of the fire was unknown. Fire crews are not expected to be able to enter the structure to begin an investigation until Saturday.