Emergency services were at the site of the substation attack and no injuries had been recorded, Odesa regional Governor Oleh Kiper said on Telegram on Wednesday.
DTEK, a large private energy company, said one of its substations had been damaged and crews were awaiting word that it was safe to begin repairs.
The company said the region had been under Russian attack "almost round the clock".
Energy infrastructure has been under attack in Ukraine for many months. The Black Sea port of Odesa, vital to many Ukrainian exports, and areas in the surrounding region, have been frequent targets of the Russian military in four years of conflict.
An overnight strike by Russian glide bombs killed a man in a village outside the southeastern town of Zaporizhzhia, the governor of Zaporizhzhia region, Ivan Fedorov, said.
In adjacent Dnipropetrovsk region, Russian drones and artillery attacked a string of towns nearly 40 times throughout the day, Governor Oleksandr Ganzha said.
Officials also reported drone attacks in Sloviansk, near the front line in eastern Donetsk region, and in Kherson region in the south and Sumy region on the border with Russia.
In southern Russia's Krasnodar region, falling drone debris killed a resident on the balcony of an apartment building northeast of the Black Sea port of Novorossiysk, Governor Venyamin Kondratiev said.
Reuters could not independently verify accounts from either side.
Meanwhile, Russia warned Baltic countries on Wednesday not to let Ukrainian drones use their airspace to carry out attacks on targets in Russia.
Foreign Ministry spokeswoman Maria Zakharova was speaking after a spate of Ukrainian drone attacks on Russia's Baltic ports of Primorsk and Ust-Luga, which have disrupted its oil exports.
"Without a doubt, we view the recent drone incidents as terrorist attacks against the Russian Federation, carried out against industrial and civilian facilities," Zakharova said at her weekly press conference.
"And if third countries have provided or are providing their territory for enemy drones to fly over, they must fully understand - and we are confident they do, because it has been explained to them - the risks they are exposing themselves to."
