The governor of Oryol, Andrei Klychkov, writes on Telegram that fuel has caught fire at a facility in the region following a "massive drone attack".
Images in Russian media show large smoke clouds billowing up into the night sky.
In the border region of Belgorod, Governor Vyacheslav Gladkov reports that a drone attack has killed a nine-year-old boy and injured parts of his family.
Ukraine regularly carries out attacks on targets linked to Russia's energy system and military, sometimes deep inside Russia.
Saturday's attack comes after Russia carried out a massive attack on Ukraine's power grid on Friday, with 93 rockets and up to 200 drones, according to Ukrainian reports.
