The strikes hit at least two residential buildings, killing one person and injuring six others, including a 7-year-old girl and her mother, Kyiv mayor Vitali Klitschko said.
Emergency workers were forced to battle flames to rescue civilians from the damaged buildings.
Ukrainian officials said 14 missiles were fired towards the city but most were blocked. Yuriy Ignat, spokesperson for the Ukrainian air force, said the first successful air attacks on the capital since 5 June were Kh-101 cruise missiles fired from warplanes over the Caspian Sea, around 1,500km (930 miles) away.
Dozens of strikes were fired across Ukraine over the weekend, many in areas that had not been targeted recently. Other targets included the central city of Cherkasy, where officials said one person was killed, and Kharkiv.
Russia's defence ministry said it hit military targets in Chernihiv in the north and Lviv in the west. Ukraine said some of the latest round of missiles were fired from Russian long-range Tu-22 bombers deployed from Moscow ally Belarus for the first time.
Mr Klitschko said the airstrikes were "maybe a symbolic attack" ahead of a Nato summit in Madrid that starts tomorrow. Lt Gen Ben Hodges, a former commander of US forces in Europe, said Russia meant to send a signal to the leaders of G7 nations meeting hours later in Germany.
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