The fire broke out just after midnight at the Utumishi Girls' Academy Senior School in Gilgil in west-central Kenya and burned for more than two hours, Education Minister Julius Migos told reporters.
He said 79 other students were injured, although 71 of them had already been discharged from hospital.
Students at the school are aged between 15 and 18 years.
"Investigations are ongoing but the ... cause of the fire is not yet identified," Migos said.
Speaking to reporters at the school, Interior Minister Kipchumba Murkomen urged people not to speculate on the cause of the fire.
However multiple survivors told first responders that a student had lit a mattress with a match, said one first responder who asked not to be named because they were not authorised to speak to the media.
They did not know what the student's motive might have been.
Fires are common at Kenyan schools, with more than 100 recorded in 2024, according to the government.
Many fires are set by students protesting harsh discipline and poor conditions, researchers say.
Doors on the second floor where the fire started were initially locked and some students died while jumping out of the windows, the first responder said.
The fire broke window panes and left the walls of the school stained with smoke.
Outside the school on Thursday, hundreds of family members gathered to seek news of their loved ones.
Injured students could be seen, some limping with bandaged limbs, others carried by police officers.
Local resident Wambui Nderitu said she had rushed to the school about 4am to look for her aunt's daughter.
"Fortunately, I found her child but she was slightly injured. She told me she was on a lower dormitory, which is how she managed to get out," Nderitu told local broadcaster Asulab TV.
"Many of those who were upstairs jumped from the balcony."
Another local resident Leah Wanjiru told Asulab TV: "I heard children screaming ... so I went outside to check and saw that the school was on fire ... We started fetching water, trying to help put out the fire and rescue people."
A fire in 2024 at a primary boarding school in nearby Nyeri County killed 21 students.
Its cause was never conclusively established.
In the worst school fire of recent times, 67 schoolboys were killed in 2001 at Kyanguli Secondary School outside Nairobi, an incident the authorities attributed to arson.
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