Odesa regional authorities said electricity for the city’s population will be restored “in the coming days”, while complete restoration of the networks may take two to three months.
As the war in Ukraine enters its 11th month, Russia continues to target civilian infrastructure.
In Kherson, two people were killed and another five wounded after Moscow's troop shelled Ukraine's southern region.
The governor of the city said the strikes destroyed a maternity ward, a cafe, as well as an apartment building.
Approximately 20 air attacks and more than 60 rocket attacks hit targets across Ukraine between Friday and Saturday, the Ukrainian military’s General Staff reported.
For the past few weeks, Russia has concentrated all its forces on trying to capture the city of Bakhmut.
There, fierce fighting has descended into bloody trench warfare, reminiscent of World War I.
According to Ukrainian President Volodymyr Zelenskyy, Bakhmut has been reduced to a "burned ruin."
Zelenskyy also said that more than 1.5 million people were without power in the southern Ukrainian city of Odesa after a night attack by drones.
The Odesa regional administration’s energy department said Saturday that fully restoring electricity could take as long as three months, and it urged families whose homes are without power to leave the region if possible.
Confusion surrounds the situation in the Russian-occupied city of Melitopol after a Ukrainian attack on a barracks.
Ukrainian officials have claimed scores of Russian casualties while Moscow says only a handful of people were injured.
Video footage posted on social media showed what was claimed to be a Russian barracks in the southern city engulfed in a fierce blaze.
Explosions were also reported overnight in the Russian-occupied Crimea including Sevastopol and Simferopol.