Poland says it has activated its air force to ensure the safety of Polish airspace after strikes also targeted the Ukrainian border region of Lviv.
The attacks started in the capital at 05:00 (03:00 GMT).
The Ukrainian military said its air defence systems were engaged in repelling the attack.
Serhiy Popko, head of Kyiv’s military administration, said about a dozen Russian missiles had been destroyed over the capital and its vicinity.
There have been no reports of casualties or major damage as a result of the attacks, he added in a statement on Telegram.
Andriy Sadovyi, Lviv’s mayor, said on Telegram that the city itself had not been hit. However, around 20 missiles and seven attack drones had been launched against the broader Lviv region, targeting “critical infrastructure”.
Ukraine was earlier placed under nationwide alert that warned of cruise missiles being launched from Russian strategic bombers.
Meanwhile, the Operational Command of the Polish armed forces (RSZ) said: “Polish and allied aircraft have been activated.
“All necessary procedures to ensure the security of Polish airspace have been activated and the RSZ is monitoring the situation continuously,” it added.
Residents in Kyiv have been pictured taking shelter in metro stations.
It comes after Russia fired dozens of missiles on Friday, hitting a dam and leaving a million Ukrainians without power.
Moscow has not yet commented on Sunday’s strikes.
The Russian-installed governor of the port of Sevastopol, in annexed Crimea, said Russian forces had shot down 10 Ukrainian missiles over the city late on Saturday.
An office building and a gas line were destroyed and a woman suffered a shrapnel injury, Mikhail Razvozhayev said on Telegram.