At least nine airports in central and western Russia temporarily halted traffic, while the strikes prompted schools in the southwestern Saratov region to close.
Strikes in the border region of Bryansk caused explosions at a refinery, ammunition depots and a chemical plant said to produce gunpowder and explosives, a Ukrainian security source told the BBC.
But Kyiv also struck far deeper into the country, with the General Staff claiming to have hit targets up to 1,100km (700 miles) from the border.
In the western region of Saratov, officials reported a “massive” drone attack.
Two industrial plants in the cities of Engels and Saratov were damaged, regional governor Roman V. Busargin wrote on Telegram.
Students were taught online on Tuesday after local schools were closed.
Last week, Kyiv said it had struck an oil storage facility in Engels – prompting a days-long effort to tackle the blaze and Busgarin to declare a state of emergency.
Officials in the western region of Tula also reported an overnight attack, where regional governor Dmitry V. Milyaev Russian said air defences had shot down 16 drones.
There were no casualties, he said, although falling debris had damaged some cars and buildings.
Elsewhere, a gas storage site near Kazan was struck in a drone attack in the southwestern region of Tatarstan, local officials said, without reporting any casualties.
Moscow also launched dozens of drones across Ukraine overnight, with multiple air raid alerts in and around Kyiv.
Ukraine’s Air Force said it had shot down around 60 of the 80 drones involved in the attack, which caused no casualties.