Debris from a drone shot down by Russia sparked a fire at the Tuapse refinery that has since been put out.
There were no casualties, the Krasnodar regional administration said on the Telegram messaging app.
It was not immediately clear if the refinery was operational or the extent of the damage it had sustained.
Russia's defence ministry earlier said its air defence systems destroyed 75 drones launched by Ukraine, including eight near the Tuapse.
The Tuapse refinery, owned by oil major Rosneft, has been a target of several Ukrainian air attacks since the start of the war that Russia launched against its smaller neighbour in 2022.
Ukrainian strikes on the Donetsk region were said to have killed at least two people. (AP PHOTO)
Earlier on Monday, the defence ministry said 47 drones were downed over the Rostov region in Russia's southwest, 17 over the waters of the Black and Azov seas, eight over the Krasnodar region, where Tuapse is located, and single drones over the Belgorod, Voronezh and Smolensk region.
Vasily Golubev, governor of the Rostov region, said on Telegram that no one was injured as a result of the attack and there was no serious damage detected.
There was no immediate comment from Ukraine.
At least two people were killed on Sunday in Ukrainian strikes on the partly Russian-occupied Donetsk region, Russian state media said, while Ukrainian officials said Russian strikes wounded at least five people.
Along the front line in the east, Russia said it had taken control of two villages - one in the Kharkiv region and one in the Luhansk region.
Ukrainian shelling of Russian-held areas of the Donetsk region killed two people in the village of Horlivka, Russian state news agency RIA Novosti said.
Three people were wounded by Russian drone strikes in southern Ukraine's partly occupied Kherson region, local officials said on Sunday morning.
In the country's northeast, officials in the Kharkiv region said two people were wounded when a village was hit by Russian shells.
11°C