Foreign Minister Dmytro Kuleba said schoolchildren had to run for cover during the assault
The side of the building, which held an art academy's gym and exhibition hall, was reduced to rubble in an area packed with high-rise apartment blocks.
The air force said it shot down two ballistic missiles fired from the occupied Crimean peninsula, more than 500km away.
CCTV footage obtained by Reuters showed the moment the blast wave blew out a window and upended shelves in a coffee shop that nearly fell on top of a barista working there.
The woman, Maria Yestafieva, told Reuters she had narrowly escaped serious injury.
"I heard glass being blown out. I was lucky to be wearing a hoodie. I put the hood on and kneeled to take cover under the counter," she said.
"I tried to squeeze in as much as possible, but there is a fridge under the counter so there wasn't enough room ... I wasn't hurt much. Just my hand (got cut) and my hoodie was ripped."
I am grateful to Ukraine's State Emergency Service rescuers, police, utility workers, and all other services involved in rescue and recovery following Russia's attack on Kyiv this morning. — Volodymyr Zelenskyy / Володимир Зеленський (@ZelenskyyUa) Russian terrorists launched ballistic missiles at Kyiv. Unfortunately, houses in a… pic.twitter.com/XFvvR4qQL2March 25, 2024
Missile debris came down in the capital's Solomyanskyi, Holosiyivskyi and Darnytskyi districts, the Kyiv city administration said.
The street outside the building was littered with bricks and cars coated in a thick layer of dust.
Kyiv's air alert system, which usually gives ample advance warning of danger, only sounded about a minute before the first of several explosions were heard by Reuters reporters.
A woman working in the building was wounded, acting culture minister Rostyslav Karandieiev said.
"Nobody died according to preliminary information," he added.
At least nine others were injured in the district, Kyiv mayor Vitali Klitschko said.
President Volodymyr Zelenskiy called on Ukraine's allies to supply more air defences.
Russia, which has stepped up its missile and drone strikes over the past week, staged its biggest attack on Ukraine's energy system in more than two years of war on Friday, according to Ukrainian officials.
Russia made no immediate comment on Monday's attack but has said it does not target civilians or civilian facilities.
Andriy Yermak, the Ukrainian president's chief of staff, described Russia and its president as "terrorists" and compared them in a statement to the Islamic State group which claimed responsibility for a deadly shooting in Moscow on Friday.
US ambassador to Kyiv Bridget Brink said Russia had used hypersonic missiles to attack the Ukrainian capital.
"Over the last five days, Russia has launched hundreds of missiles and drones against a sovereign country," Brink said.
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