Children and staff at the school were in shelters when the drone hit, Kyiv mayor Vitalii Klitschko said on Thursday, although the drone's warhead did not explode.
There was no immediate report of casualties.
The building's brick frontage showed a large hole and black burn mark alongside smashed windows.
Kyiv has in recent weeks lived through repeated air raid alerts, punctuated by loud bangs and palls of black smoke as drones and missiles hit, making it feel like a city under siege.
The Russian onslaught aims to terrorise civilians, officials and analysts say, and break their will to resist four-and-a-half years after Moscow's full-scale invasion.
The strain is showing among Kyiv residents.
Maryna Lystopad, 35, said her hair has started falling out due to the strain of escalating attacks and never knowing where a drone or missile will hit.
"It's really horrible. I can't take it anymore. I think, I think that soon we're all going to leave. I'm really not doing well," she told The Associated Press.
"I'm constantly anxious. I can't relax," she said.
"I keep thinking that if something happens, if something hits, one of my relatives could be killed."
She recently had to go to another part of the city, she said, and was "genuinely stressed the whole way there".
"I kept checking, like, whether anything was flying in, where it was going, where am I supposed to go? Where am I supposed to run?"
The war on the ground has not seen major shifts since 2025, but Ukraine is struggling to fend off Russia's intensified aerial attacks on cities that include speedy ballistic missiles and high-flying jet-powered drones.
In response, Ukraine has fired its long-range drones at manufacturing plants deep inside Russia and has targeted Russia's drone launch sites.
Ukrainian President Volodymyr Zelenskiy said Kyiv's forces struck a site in Russia's southwestern Oryol region that is used to store and launch attack drones.
To turn the tide, Ukraine needs US-made Patriot missiles that can effectively defend against ballistic missiles, but they are in short supply since the Iran war began.
A plan to produce them inside Ukraine could take years to bear fruit.
Kyiv is racing to produce new interceptors that can bring down fast-moving jet-propelled drones as the swift cycle of military innovation during the war continues.
Ukraine also wants tougher sanctions imposed on Russia to prevent it getting key high-tech components for its arsenal.
Moscow, meanwhile, is pressing its advantage before Ukraine comes up with an answer to the latest challenges.
Ukrainian officials did not report any energy infrastructure being hit on Thursday, a day after what officials said was the biggest Russian attack on the power grid since spring 2025.
The Institute for the Study of War, a Washington-based think tank, said Wednesday's barrage marked "the beginning of Russia's strike campaign aimed at degrading Ukraine's energy security ahead of winter ... and forcing Ukraine to capitulate".
Russia is expected to step up attacks on the electricity supply as the weather gets colder.
It was 19C in Kyiv on Thursday, and mild temperatures were set to continue.
In a surprise development, Russia used a new jet-powered drone for the first time on Wednesday, fitting it with a warhead designed to sever high-voltage pylons, said Serhii Beskrestnov, an adviser to Ukraine's president on defense technology.
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