The attack sparked a massive fire, Ukraine's general staff said on the Telegram app.
Earlier, industry sources said a Ukrainian drone attack sparked a fire at the oil terminal of Russia's Black Sea port of Novorossiysk.
Ukraine has intensified aerial attacks on Russia's energy infrastructure, including ports, in an effort to reduce Russian revenues from the sales of oil, the lifeblood of the economy.
According to the sources, the blaze engulfed the key pier of Russia's oil pipeline monopoly Transneft near the berths 1, 1a and 2.
Berth 1 is able to service tankers with deadweight of up to 250,000 metric tons, while berth 2 can load tankers of up to 90,000 tonnes of deadweight, according to sources.
The effect on loading operations from the attack is not immediately clear.
Transneft did not reply to a request for comment.
Separately, Russian authorities said on Monday said that Ukrainian drones attacked the Caspian Pipeline Consortium's Black Sea terminal, which handles 1.5 per cent of global oil supply, damaging the single point mooring (SPM), loading infrastructure and four vast storage tanks.
Ukraine did not immediately reply to a request for comment and Reuters was unable to independently verify the Russian defence ministry statement.
CPC declined to comment.
Russia's defence ministry said Ukraine had attacked the CPC's loading facilities with air drones.
The CPC's Yuzhnaya Ozereevka terminal exports oil from Kazakhstan and its shareholders include Chevron and Exxon Mobil.
"The Kyiv regime deliberately attacked facilities of the international oil transportation company Caspian Pipeline Consortium in order to inflict maximum economic damage on its largest shareholders - energy companies from the United States and Kazakhstan," the defence ministry said in a statement.
The CPC terminal, located to the south-west of Novorossiysk, handles 80 per centr of Kazakhstan's crude exports.
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