The drones were intercepted overnight over the province, Belgorod Gov. Vyacheslav Gladkov said in a Telegram post, AP reported.
He said that no one had been hurt, but unspecified administrative buildings, residential buildings, and cars were damaged.
Ukrainian officials made no immediate comment.
Russia said the previous day that it beat back one of the war’s most serious cross-border attacks, with the Defense Ministry saying that more than 70 attackers were killed in a battle in Belgorod that lasted around 24 hours. It made no mention of any Russian casualties.
Russian Defense Ministry spokesman Igor Konashenkov said that local troops, airstrikes, and artillery routed the attackers. Twelve local civilians were wounded in the attack, officials said, and an older woman died during an evacuation.
Details of the incident in the rural region, lying about 80 kilometers (45 miles) north of the city of Kharkiv in eastern Ukraine and far from the front lines of the almost 15-month war, are unclear.
Moscow blamed the incursion that began Monday on Ukrainian military saboteurs. Kyiv described it as an uprising against the Kremlin by Russian partisans.
The region is a Russian military hub holding fuel and ammunition depots. The Belgorod region, like the neighboring Bryansk region and other border areas, has witnessed sporadic spillover from the war.
Elsewhere, the Ukrainian General Staff said Wednesday that “heavy fighting” is continuing inside Bakhmut, days after Russia said that it completely captured the devastated city.
The head of the Russian private army Wagner says his force lost more than 20,000 fighters in the drawn-out battle for Bakhmut, with about 20% of the 50,000 Russian convicts he recruited to fight in the 15-month war dying in the eastern Ukrainian city.
Bakhmut lies in Donetsk province, one of four provinces Russia captured last fall. The nine-month battle for Bakhmut has killed tens of thousands of people as Ukraine pursues its strategy of grinding down the Kremlin’s forces.