The dead included 19 girls and five boys, said Dunia Masumbuko Bwenge, vice governor of South Kivu province, where Bukavu is located, in the government appointed by the AFC/M23 movement.
The AFC/M23 said in a statement that the provisional death toll stood at 24 and that an investigation into the cause and circumstances of the blaze was under way.
The group said 29 people were receiving medical treatment, including 21 in intensive care.
The rebels seized Bukavu during a lightning advance across eastern DR Congo early last year.
Bwenge said 29 people were injured in the blaze and investigations were ongoing to determine the cause of the fire.
The fire was out by Thursday afternoon but white smoke was still rising from piles of rubble and twisted corrugated metal sheets, a Reuters witness said.
"We were on the avenue and the children had just gone to school when the fire started not far from the school," witness Pierre Mudahama said.
"Ambulances arrived to take away the bodies and the injured."
The final death toll could rise, residents and health workers said.
One man at the scene told Reuters that he had helped to load 17 dead bodies - men in addition to children - into an ambulance.
A local health centre said it had received 10 bodies of people killed in the fire.
Another hospital said it had admitted more than 50 students, 14 of whom died.
