Ukrainian officials said four people were killed and at least 22 wounded in the capital overnight.
Russia did not say where Oreshnik hit, but Russian media and military bloggers said it targeted a huge underground natural gas storage in Ukraine's western Lviv region.
Russia's defence ministry said the attack was a retaliation to what Moscow said was a Ukrainian drone strike on Russian President Vladimir Putin's residence in December.
Ukraine and US President Donald Trump have rejected the Russian claim of the attack on Putin's residence.
Lviv Mayor Andriy Sadoviy said that Russia struck critical infrastructure with a ballistic missile, but did not give details.
He said the missile travelled at a speed of 13,000km/h, and the specific type of rocket was being investigated.
Russia first tested the Oreshnik - Russian for hazelnut tree - to strike a Ukrainian factory in November 2024.
Putin has bragged that Oreshnik's multiple warheads plunge at speeds of up to mach 10 and cannot be intercepted, and that several of them used in a conventional strike could be as devastating as a nuclear attack.
Oreshnik can also carry nuclear weapons.
The Russian leader has warned the West that Russia could use the Oreshnik next against allies of Kyiv that allowed it to strike inside Russia with their longer-range missiles.
After the overnight strike on Ukraine's capital, those killed included an emergency medical aid worker, said Kyiv City Military Administration head Tymur Tkachenko.
Five rescue workers sustained injuries while responding to the site of ongoing attacks, Ukraine's security service said.
Several districts in Kyiv were hit in the attack, said Kyiv City Military Administration head Tymur Tkachenko.
In the Desnyanskyi district a drone crashed onto the roof of a multistorey building.
At another address in the same district the first two floors of a residential building were damaged.
In Dnipro district, parts of a drone damaged a multistorey building and a fire broke out.
Running water and electricity were disrupted in parts of the capital as a result of the attack, Kyiv Mayor Vitali Klitschko said.
The attack took place just hours after Ukrainian President Volodymyr Zelenskiy alerted the nation about Russia's intentions for a large-scale offensive.
He said Russia aimed to take advantage of the frigid weather in the capital, making roads and streets perilously icy.
24°C