The blaze injured another 36 people, some of them critically, Japanese authorities said. Most were workers at Kyoto Animation, known for mega-hit stories featuring high school girls.
The fire started in the three-story building in Japan's ancient capital after the suspect sprayed an unidentified liquid accelerant, Kyoto prefectural police and fire department officials said.
Thirteen were confirmed dead on the first and second floors, Kyoto fire department official Kazuhiro Hayashi said. On the third floor, more than 10 people were found unresponsive, he said. Some of them were found on the stairs, where they apparently collapsed while gasping for air and trying to go out to the roof.
Hayashi says firefighters were still searching inside the building in case anyone else was left behind.
The suspect was injured and taken to a hospital, officials said. Police are investigating the man on suspicion of arson.
Survivors who saw the attacker said he was not their colleague and that he was screaming "(You) die!" when he dumped the liquid and started the fire, according to Japanese media reports. They said some of the survivors got splashed with the liquid.
Footage on Japan's NHK television showed gray smoke billowing from the charred building. Other footage showed windows blown off.
"There was an explosion, then I heard people shouting, some asking for help," a female witness told TBS TV. "Black smoke was rising from windows on upper floors, then there was a man struggling to crawl out of the window."
Witnesses in the neighborhood said they heard bangs coming from the building, others said they saw people coming out blackened, bleeding, walking barefoot, Kyodo News reported.
Rescue officials set up an orange tent outside the studio building to provide first aid and sort out the injured.
Fire department officials said more than 70 people were in the building at the time of the fire and many of them ran outside.
Kyoto Animation, better known as KyoAni, was founded in 1981 as an animation and comic book production studio, and its hits include "Lucky Star," ''K-On!" and "Haruhi Suzumiya."
With at least 23 killed or presumed dead, the fire was the worst mass killing in Japan since a man stabbed and killed 19 people at an assisted living facility in western Tokyo in 2016.
A fire in 2001 in Tokyo's congested Kabukicho entertainment district killed 44 people in its worst known case of arson in modern times. Police never announced an arrest for setting the blaze, though five people were convicted of negligence. In 2008, 16 people died in a blaze at a movie theater in Osaka, near Kyoto.