The fire blocked the only exit to Darul Quran Ittifaqiyah and the students and teachers were trapped behind barred windows.
Firefighters rushed to the scene after receiving a distress call at 5:41am and took an hour to put out the blaze, which started on the top floor of the three-storey dormitory, Kuala Lumpur Police Chief Amar Singh said.
There were at least 23 charred bodies, he said, 21 of them boys aged between 13 and 17, and two teachers.
Mr Singh said 14 other students and four teachers were rescued, with six of them hospitalised in critical condition.
The fire broke out near the only door to the boys' dormitory, trapping the victims, fire department senior official Abu Obaidat Mohamad Saithalimat said.
The cause was believed to be an electrical short-circuit, he said.
Noh Omar, Malaysia's minister for urban well-being, housing and local government, said a wall separating the victims from a second exit "shouldn't have been there".
He said the school's original architectural plan included an open top floor that allowed access to two exit staircases.
But a wall was built dividing that floor, leaving only one exit for the dorm, he said, adding that the school submitted an application for a fire safety permit that hadn't been approved.
Another fire department official, Soiman Jahid, said firefighters heard shouts for help when they arrived at the school.
He said they found 13 bodies huddled in a pile on the right corner of the dorm, another eight on the left corner of the dorm and one in the middle, near the staircase.
Mr Soiman said initial investigations showed the school had just submitted an application to the city council for building safety approval, but he could not give further details.
A fire department official, who declined to be named because he was not authorised to give a statement, said the bodies were piled on top of each other, indicating a possible stampede as people tried to flee the fire.
The official had earlier said 25 bodies were found, but the more recent tally of dead and injured matches the number of people thought to have resided there.
Mr Singh said police were still finalising the details and investigating the cause.
Local media showed pictures of blackened bunk bed frames in the burned dormitory.
Nearby resident Nurhayati Abdul Halim told local media she saw the boys crying and screaming for help when the fire broke out.
"I saw their little hands out of the grilled windows; crying for help," she said.
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