The Sumy region borders Russia's Kursk region and has been regularly shelled by Russian forces for months.
"Russians dropped a bomb on a residential building. Two children and one adult were injured. One entrance of the apartment building was destroyed," Sumy's military administration said on Telegram.
A rescue operation was under way to find people who may be trapped by rubble, officials said.
Russia, which began its full-scale invasion of Ukraine in February 2022, did not immediately comment on the events in Sumy.
Meanwhile, Ukrainian President Volodymyr Zelenskiy says Russian and North Korean forces have suffered heavy losses in fighting in Russia's southern Kursk region.
Ukrainian and Western assessments say some 11,000 North Korean troops are deployed in the Kursk region, where Ukrainian forces occupy swathes of territory after staging a mass cross-border incursion in August.
"In battles yesterday and today near just one village, Makhnovka, in Kursk region, the Russian army lost up to a battalion of North Korean infantry soldiers and Russian paratroops," Zelenskiy said. "This is significant."
A battalion can vary in size but is generally made up of several hundred troops.
Zelenskiy last week reported heavy North Korean losses in the Kursk region, saying their forces were not being protected by the Russian forces they are fighting alongside.
He said North Koreans were taking extreme measures to avoid being taken prisoner and in some instances were being executed by their own forces.
In his latest remarks, Zelenskiy also said "fierce battles" had raged along the entire 1,000-km front line, with the most difficult situation near the city of Pokrovsk.
Russian forces, he said, "continue to expend vast numbers of their own personnel in assaults".
Pokrovsk, home to a mine that is the sole supplier of coking coal to Ukraine's once-giant steel industry, had a pre-war population of some 60,000 people. Ukraine estimates that around 11,000 of them remain in the city.
Operations at an airport in the Russian city of St Petersburg were reinstated on Saturday evening after they were temporarily suspended for safety reasons.
The Russian defence ministry reported that 16 Ukrainian drones were destroyed overnight over the regions of Bryansk, Smolensk, Belgorod, Pskov and Leningrad - the area surrounding St Petersburg.
There have been repeated restrictions at airports in Russia in connection with Ukrainian drone attacks.
Due to the deployment of Russian air defence, take-offs and landings are sometimes not possible.
According to the Ukrainian air force, Ukraine repelled 81 drone attacks by Russia during the night.
Of these, 34 drones were shot down and the location of 47 was lost, mostly due to the use of electronic defence systems.
The drones that were shot down damaged private homes in the Chernihiv and Sumy regions.
with DPA
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