They said two ballistic missiles were intercepted, but seven people were injured as debris fell.
Explosions were heard across the Ukrainian capital and a column of smoke was seen rising in the east.
The city’s mayor urged residents to immediately take cover as the attack came virtually without warning.
Moments before the explosions the Ukrainian air force warned in a message on Telegram that a missile was flying towards the city.
It is unusual to have such attacks without an air raid alert.
Kyiv Mayor Vitali Klitschko wrote on his Telegram channel: “Explosions in the capital. Urgently to the shelter!”
Ukraine’s foreign minister, Dmytro Kuleba, posted videos online purporting to show school children running to a shelter.
The country’s air force commander said Russia fired two ballistic missiles from Crimea, which was annexed by Moscow, but both were intercepted by air defences.
Following a string of explosions, missile debris came down in the Pechersky district, not far from the centre of Kyiv, and several other areas.
The attack is the third on Kyiv by Russia in five days.
Latest reports say ten people including a teenage girl were injured. Two people were taken to hospital.
A Kyiv resident, Oksana, said she was at work when she first heard the air raid sirens followed by the sound of explosions.
She told the AFP news agency: “Before I could do anything, the first explosion hit, There was a cloud of dust, smashed cars, windows, everything.”
Another resident, Roman, told the BBC: “The blasts – which were very loud, happened right after the capital’s air raid sirens had started sounding.”
The US ambassador in Kyiv, Bridget Brink, said on social media that Russia had used hypersonic missiles to attack the Ukrainian capital.
She added that there was “not a moment to lose” as Ukraine needed American assistance now, alluding to a $60bn military aid package which has been held up in the US Congress.
President Volodymyr Zelensky said the attack showed again that Ukraine needed better air defence systems from its allies.
In a social media post, Mr Zelensky said: “It means safety for our cities and saved human lives. All of us in the world who respect and protect life need to stop this terror.”
Overnight there were also drone attacks on Odesa and Mikolayiv in the south of Ukraine, hitting energy infrastructure and leaving some areas without electricity.
The latest assault on Kyiv comes after Ukraine said it had hit two landing ships, a communications centre and other infrastructure used by Russia’s Black Sea fleet off Crimea on Sunday.
The Ukrainian general staff said the Yamal and Azov ships had been destroyed.
The BBC, however, has not been able to verify the Ukrainian claim to have damaged the ships, which are designed to land troops and equipment straight to shore without the need for a pier or dock.
On the same day, one of Russia’s cruise missiles entered the airspace of neighbouring Poland, a Nato member.
Polish armed forces said in a statement that the object had stayed in Polish air space for 39 seconds. Defence Minister Wladyslaw Kosiniak-Kamysz said that if the missile had been seen to go in the direction of any targets located in Poland, then “of course, it would have been shot down and more adequate measures would have been taken”.
On Monday, Poland’s foreign ministry said that the Russian ambassador in Warsaw failed to show up for a diplomatic summons.
The ambassador, Sergey Andreyev, told Russia’s Ria Novosti news agency that he felt “it made no sense to discuss this topic without any provision of proof, and I refused to visit the Polish foreign ministry”.
There has been an increase in aerial attacks by both sides in the past few days, while Russia makes slow progress in taking some territory in the east of the country.
On Friday, Russia fired dozens of missiles at Ukraine, hitting a dam and leaving a million Ukrainians without power, in the wake of fierce Ukrainian bombardments on Russian border regions. The Russian authorities said a Ukrainian drone attack had caused a fire at a large power plant in Rostov.
Meanwhile Kharkiv – close to the Russian border – is still in partial blackout after all its power substations were destroyed by Russian attacks on Friday.