Moscow claimed it was in response to a Ukrainian strike on Russian soil using American-made weapons.
At least three loud blasts were heard in Kyiv shortly before sunrise on Friday.
Falling missile debris caused damage and sparked fires in three districts, the city administration said.
The attack knocked out heating to 630 residential buildings, 16 medical facilities, and 30 schools and kindergartens, it said.
A Russian strike damaged some buildings and knocked out heating to hundreds of others. (AP PHOTO)
The Russian defence ministry said the strike was in response to a Ukrainian missile attack on Russia's Rostov border region earlier on Friday.
That attack used six American-made Army Tactical Missile System, known as ATACMS, missiles and four Storm Shadow air-launched missiles provided by the UK, it said.
The use of Western-supplied weapons to strike Russia has angered the Kremlin.
Ukraine fired several American-supplied longer-range missiles into Russia for the first time on November 19 after Washington eased restrictions on their use.
Answering Friday's Ukrainian attack, the defence ministry said it carried out a group strike with "high-precision, long-range weapons" on the command centre of Ukraine's military intelligence agency and another location where it said Ukraine's Neptune missile systems are designed and produced.
The attack also targeted Ukrainian ground-based cruise missile systems and US-made Patriot air defence systems.
"The objectives of the strike have been achieved. All objects are hit," the defence ministry said in a Telegram post.
Its claims could not immediately be verified.
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