The Krasnodar region in the south of Russia and the Belgorod region on the border with Ukraine were particularly badly affected.
In Belgorod, a woman and her son died after a drone hit their car, according to Governor Vyacheslav Gladkov. The father and another man were injured.
According to images from the scene, a large fire also broke out at a petrol station after it was hit.
In Tuapse in the Krasnodar region, there was a major fire at an oil processing plant.
As per the eyewitness reports on social networks, a harbour and an oil depot were hit in the Black Sea city of Novorossiysk.
The local authorities reported that, however, all drone attacks had been repelled.
In the city of Sevastopol on the Black Sea peninsula of Crimea, which Russia annexed in 2014, the power went out after debris from a downed drone hit a municipal substation, according to the governor there.
The Defence Ministry in Moscow reported that Russian air defences had intercepted or destroyed 102 drones, half of which were over Crimea.
Six unmanned explosive boats were also destroyed in the Black Sea, Russia said.
Ukraine is firing at targets on Russian territory on a daily basis, over two years after the war broke out.
With Western help, the country has also significantly expanded its own drone production.