Both buildings and cars are reported to have started burning after being hit in Kyiv.
"Stay in the shelters. The massive attack on the capital continues", wrote Kyiv's mayor Vitalij Klytjko on Telegram during the night.
In the major port city of Odessa in southern Ukraine, residential buildings as well as maternity and healthcare facilities were hit, according to local authorities.
At least one person, a 59-year-old man, was killed and at least four people were injured in Odessa.
The attacks come after Russia sent a total of 479 drones and 20 rockets against Ukraine during the previous night. According to Ukraine, it was more drones than any other night in the over three-year-long war. However, the Ukrainian air defense managed to shoot down the majority of them.