Most of the victims were reportedly pupils aged between seven and 16 who lived and studied at the Zhenxing Martial Arts Centre in Henan province.
The blaze broke out early on Friday and has been put out, local authorities said, but it is unclear how it started.
Fatal fires are not uncommon in China, which has patchy safety regulations.
The person in charge of the martial arts centre has been arrested, according to a brief statement from Zhecheng county government posted on its official WeChat channel.
Government officials told Beiing Toutiao News that there were 34 boarding students at the centre when the fire broke out at 03:00 local time on Friday (19:00 GMT Thursday).
Injured students were quickly rushed to a local hospital. Parents interviewed by news agency Reuters said they were not given any information nor were they allowed to see their children yet.
“At Zhenxing, the kids would study and practice martial arts in the day and live there every night. I don’t know what caused the fire,” said the father of a nine-year-old boy who survived.
Another parent told Reuters that “all information is being blocked”.
Home of the famous Shaolin Temple, Henan province is known to be the birthplace of Chinese martial arts, where thousands of students study in kung fu training camps.
A fire at an underwear factory in southern China in 2014 killed at least 11 people and injured 15 more.
