Ukrainian prosecutors said the drone attack hit a market in Sofiiska Borshchahivka on the western outskirts of Kyiv on Sunday, killing two people and injuring about 10.
Pictures posted online showed installations and vehicles on fire, with debris strewn on the ground.
In the capital, Mayor Vitali Klitschko said nine people were injured, including a child. Six of the injured were being treated in hospital.
Russian forces have long staged intensive attacks on Kyiv and other Ukrainian cities, mostly at night. In recent weeks, they have launched strikes almost continuously throughout the day.
Ukrainian President Volodymyr Zelenskiy decried the latest attacks, saying the civilian targets made the acts unquestionably "terrorism".
"Russia has no military objective whatsoever in doing this," Zelenskiy wrote in a post on X.
"It is purely an attempt to break people and inflict as much harm as possible on our society."
In the northern city of Sumy, a frequent Russian target near the border, three glide bombs struck near a family support centre, killing two people, regional governor Oleh Hryhorov wrote on Telegram.
Russia has long said it intends to turn areas of the Sumy region into a buffer zone.
In Kharkiv, Ukraine's second-largest city in the northeast and another frequent target, a drone struck a car, killing the driver, prosecutors said.
Zelenskiy said Russia had deployed 277 attack drones of various types since Saturday, 155 of them of the jet-powered variety Moscow has recently used more readily as they fly higher and are difficult to intercept.
The targets in Kyiv included a building used as a residence by the Saudi Arabian ambassador.
Klitschko said on Telegram that a drone had struck a high-rise apartment building, triggering a fire in an eastern suburb and wounding one person. Emergency crews extinguished the blaze.
He later said a drone had hit another high-rise in a central district, with emergency services investigating possible casualties at the site.
Drones had earlier hit areas near a kindergarten and a playground in two districts, Klitschko said, and other areas in the city also suffered damage.
Ukraine's largest mobile service provider told the Interfax Ukraine news agency that Russian forces had hit its headquarters in continued strikes on Ukrainian data centres and communications infrastructure. There were no casualties.
Russia's defence ministry issued statements saying its forces had struck two data centres in Kyiv, a logistics hub in Odesa, as well as two cargo vessels headed for Odesa.
Both sides in the more than four-and-a-half-year war deny targeting civilians.
