The nearly three-year war has seen a sharp escalation in recent days, with Moscow pummelling Ukraine's energy infrastructure ahead of the winter.
Friday's drone barrage came a day after Russia launched around 90 missiles on the war-torn country, cutting power to over a million people, reports BSS.
Moscow fired 132 drones overnight, of which "88 drones were shot down" and "41 were lost, presumably due to defence countermeasures", Ukraine's air force said.
Air defences shot down drones over a dozen regions, while falling debris damaged a health care clinic in the capital Kyiv, according to the local mayor.
A drone attack killed a woman in the southern city of Kherson, the head of the local military administration Roman Mrochko said.
At least two regions suffered power cuts on Friday, Ukrainian electricity operator Ukrenergo said.
"Emergency repair works are ongoing around the clock. By the end of the day, the power company plans to restore power to the de-energised customers in Kherson and Mykolaiv regions," it said.
The latest strikes come as Ukraine enters a tough winter, with Russian forces stepping up aerial attacks and advancing on the eastern front.
Moscow said Friday it had seized the village of Rozdolne in the southern part of Ukraine's Donbas region, where it has made a string of territorial gains in recent months.
Russia downed 47 attack drones fired overnight by Ukraine, mainly targeting the Rostov border region where a major fire broke out at an industrial site, authorities said.