Police said the 41-year-old suspect broke into the Kyoto Animation studio on Thursday morning and sprayed petrol before igniting it.
The suspect has been detained and was taken to hospital with injuries.
Japan's Prime Minister Shinzo Abe said the incident was "too appalling for words" and offered condolences.
It is one of Japan's worst mass casualty incidents since World War Two.
Kyoto Animation, known as KyoAni, produces films and graphic novels, and is well regarded by fans for the quality of its productions.
How did the incident unfold?
The fire broke out at the three-storey building at about 10:30 local time (01:35 GMT) on Thursday. Rescue operations are still ongoing.
Police also found knives at the scene, say local media. Public broadcaster NHK said the man had been heard saying "drop dead" as he set fire to the building.
The suspect's relationship with the company is unclear.
Eyewitnesses described a loud explosion followed by an inferno that rapidly engulfed the building.
It took firefighters five hours to bring the blaze under control, reports said
"I saw some people with burns, covered with something. They were rushed to the ambulance," one neighbour said.
The official, Kazuhiro Hayashi, said most of the casualties had been on the stairs to the top floor, where they apparently collapsed trying to escape.
Firefighters said they had found 33 bodies, two on the first floor, 11 on the second floor and 20 on the stairs from the third floor to the top floor, he said.
Some 36 people are in hospital, some in a critical condition, reports say. About 70 people were in the building when the fire started.
Who is the suspect?
Reports say the man is not a former employee - but eyewitnesses say he appeared to be angry with the animation studio.
They said he ran away from the building towards a nearby train station after the fire started but fell to the ground. Some reports said he was pursued by employees of Kyoto Animation.
"A person with singed hair was lying down and there were bloody footprints," a 59-year-old woman living nearby told news agency Kyodo.
"He seemed to be in pain, irritated and suffering, but also angry as if he was resentful. I heard him saying something like 'You copied it'," a neighbour said.
The Asahi Shimbun newspaper quoted a 61-year-old neighbour as saying she clearly heard the man shout: "You ripped me off."
Emergency crew wheel a stretcher away from the building in the city of Kyoto
The suspect was injured and was being treated in hospital, so police could not immediately question him, NHK said.
Japanese media reports said a man in his 40s had earlier bought 40 litres (nine gallons) of petrol at a nearby petrol station. Two containers used for the fuel were later found at the scene of the fire, Asahi Shimbun newspaper reported.
Meanwhile Kyoto Animation Director Hideaki Hatta told the broadcaster that the company had recently received threatening emails.
"They were addressed to our office and sales department and told us to die," he said.
Mr Hatta told reporters that he was "heartbroken" at the attack.
"It is unbearable that the people who helped carry Japan's animation industry were hurt and lost their lives in this way," he said.
What do we know about the studio?
Kyoto Animation, known as KyoAni, was founded in 1981 and has produced popular animation shows including K-On and The Melancholy of Haruhi Suzumiya.
The studio also released a standalone feature anime A Silent Voice in 2016.
One of KyoAni's series, Violet Evergarden, was picked up by Netflix for a global market.
Floral tributes have been left outside the building as people pay their respects to the victims
It also publishes many popular graphic novels, mainly about teenage school life.
The studio is known for paying its animators a regular salary, breaking with the industry's standard of paying per frame - which is seen as putting extreme pressure on staff.
It is also the first successful studio outside Tokyo, Prof Ryusuke Hikawa from Meiji University told NHK.
Source: BBC https://bbc.in/2JCqllD