The mayor of Kyiv has told residents not to leave shelters
A number of bombings have hit Kiev and Ukraine has been put on high alert as Russia has carried out airstrikes.
Poland says it has activated its air force to ensure the security of Polish airspace after attacks also took place on the Ukrainian border region of Lviv.
The attacks began at 05:00 (03:00 GMT) in the capital.
Ukraine's military said its air defense systems were engaged in repelling the attack.
About a dozen Russian missiles were destroyed in and around the capital, Kyiv's military administration chief Serhiy Popko said.
There were no reports of casualties or major damage from the attacks, he added in a statement on Telegram.
Lviv's mayor Andriy Sadovy said in a telegram that the city itself was not affected. However, some 20 missiles and seven attack drones were launched against the wider Lviv region, targeting “critical infrastructure”.
Ukraine was earlier placed on nationwide alert after being warned of possible missile launches from Russian strategic bombers.
Meanwhile, the Operations Command of the Polish Armed Forces (RSZ) said: “Poland and allied aircraft have been activated.
“All necessary procedures to ensure the safety of Polish airspace have been implemented and RSZ is constantly monitoring the situation,” it added.
Residents of Kiev have been filmed taking shelter in metro stations.
Moscow has yet to comment on Sunday's strikes.
The Russian-installed governor of the port of Sevastopol in annexed Crimea said late Saturday that Russian forces shot down 10 Ukrainian missiles over the city.
An office building and a gas line were destroyed and a woman was slightly injured, Mikhail Razvozhayev said in Telegram.
