Amid the attack, air raid sirens sounded across the country as officials feared another large-scale missile attack from Moscow.
Odesa Governor Maksym Marchenko said an infrastructure target was hit, via a post on Telegram.
He also warned about the threat of a "massive missile barrage on the entire territory of Ukraine".
Meanwhile, multiple explosions were reported in Dnipro, where two infrastructure objects were damaged and at least one person wounded, the deputy head of Ukraine’s presidential office, Kyrylo Tymoshenko, said.
According to Kyiv Governor Oleksiy Kuleba, air defense systems were operating in the country's central region.
Officials in the Poltava, Kharkiv, Khmelnytskyi and Rivne regions also urged residents to stay in bomb shelters amid the persisting threat of missile strikes.
The strikes on the Odessa region follows the huge barrage of Russian strikes on Tuesday - the biggest attack to date on Ukraine's energy infrastructure.
Two people were also killed in Poland during the attack, after a missile landed within the country's borders.
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Initially, some accusations were levelled at Russia for the missile, but Poland has now said it appeared to be unintentional and was probably launched by air defences in neighbouring Ukraine.
Russia has increasingly resorted to targeting Ukraine’s power grid as winter approaches and its battlefield losses mount.
The most recent barrage followed days of euphoria in Ukraine, which was sparked by one of its biggest military successes - the retaking of the southern city of Kherson.
Andriy Yermak, the head of Ukraine’s presidential office, called the strikes on energy targets "a naive tactics of cowardly losers" in a Telegram post on Thursday.
"Ukraine has already withstood extremely difficult strikes by the enemy, which did not lead to results the Russian cowards hoped for," Mr Yermak wrote.