The assault was carried out using 14 bomber planes in the early hours of Thursday, Polish state news agency PAP reported.
Kyiv's military administration said preliminary information indicated all incoming missiles had been destroyed, British broadcaster BBC reported.
Officials said the air attacks were "unprecedented in their power, intensity and variety."
Meanwhile, one person was killed and two more injured in a missile attack on the southwestern Black Sea port city of Odesa, according to officials.
Russian missiles struck an industrial facility on the outskirts of Odesa and injured two guards working there, The Kyiv Independent website reported.
Explosions were also heard in central regions of Vinnytsia, Khmelnytsky and Zhytomyr, according to the BBC.
In Khmelnytsky, an infrastructure facility was damaged, but there were no casualties, the region’s military administration said.
Before the all-clear was given in Kyiv, Mayor Vitali Klitschko said a fire had broken out in a garage in the Darnytsya area of the city, but added that no one had been injured, the BBC reported.
Meanwhile, the head of Kyiv's city military administration, Serhiy Popko, said that a heavy missile attack had been launched from Russian strategic bombers over the Caspian Sea, and probably included cruise missiles.
Popko also said that Russia had deployed reconnaissance drones over Kyiv after the latest wave of air strikes, according to the BBC.
A second fire broke out in a non-residential building in the capital's eastern Desnyansky district, officials told reporters.
Andriy Nebytov, the head of police in the Kyiv region, said no significant damage was recorded from falling missile debris, nor were there any casualties, according to the Kyiv Independent.
Ukraine downs 29 Russian missiles: officials
Later on Thursday morning, Ukraine’s General Staff said that the country’s air defence “successfully shot down 29 Russian missiles, two kamikaze drones, and two reconnaissance drones on May 17-18,” The Kyiv Independent reported.
In all, Russia launched 22 long-range X-101/X-555 missiles from two Tu-160s and eight Tu-95s bombers, six Kalibr cruise missiles from the Black Sea, and two Iskander missiles from ground-based operational-tactical missile systems, according to Ukraine’s General Staff.
Ukraine's air defence downed 25 Russian missiles, including six Kinzhal ballistic missiles, during a previous air attack on May 16, officials said.
Russia was able to inflict slight damage on Ukraine’s US-made Patriot air defence system, according to news outlets.
Black Sea grain deal extended for two months
Meanwhile, an agreement enabling Ukraine to export millions of tonnes of grain through the Black Sea despite the ongoing Russian invasion was prolonged for a further two months on Wednesday, Ukraine’s Interfax news agency reported.
The two-month extension was negotiated by the United Nations and Turkey, and was announced a day before the previous deal was due to expire, according to news outlets.
There had been concerns that Russia could pull out of the deal, the BBC reported.
Thursday is day 449 of Russia’s war on Ukraine.
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Source: PAP, Reuters, BBC, The Kyiv Independent, Interfax-Ukraine