The overnight attack was the latest in Moscow's winter campaign of strikes on Ukrainian energy infrastructure, with Kyiv under pressure to agree to a US-backed peace deal to end the nearly four-year war.
Ukraine's President Volodymyr Zelenskiy said on Tuesday Russia had launched more than 50 drones at Odesa in what he described as a "brutal" attack on the city, as Ukrainian and Russian negotiators prepare for new talks on Sunday.
"Every such Russian strike erodes the diplomacy that is still ongoing and undermines the efforts of partners who are helping to end this war," Zelenskiy wrote on X.
Odesa Governor Oleh Kiper said two children and a pregnant woman were among the wounded in the strikes on the city. Dozens of residential buildings, a church, a kindergarten and a high school were damaged, he said.
By midday on Tuesday, rescue workers were still digging through a mountain of rubble outside a building where emergency officials said two residents had been killed. It was ripped open across several floors.
Resident Denys Tsybulskiy stood outside the building trying to reach his neighbour, who he said was trapped under the debris but had showed signs of using his phone.
"He can't pick up the phone, he can't talk, but there's hope that he's laying there," he said.
The overnight attack also led to the "colossal destruction" of an energy facility in the city, leading private power provider DTEK said in a statement.
Odesa, on Ukraine's strategically critical Black Sea coast, has come under increasing attack in recent months.
In Ukraine's second-largest city of Kharkiv, Governor Oleh Syniehubov said late on Monday that a combined Russian missile and drone attack had knocked out power to about 80 per cent of the city and the surrounding region after an energy facility suffered "quite serious damage".
In comments to Ukrainian television on Tuesday, Kharkiv's mayor, Ihor Terekhov, said about 40 per cent of consumers had no electricity.
Ukraine's air force said Russian troops had launched 165 drones overnight - 135 of them neutralised by Ukrainian air defences.
In western Ukraine's Lviv region, which borders NATO-member Poland, an infrastructure facility also came under Russian attack in the city of Brody, local officials said.
The city council reported heavy smoke and an unpleasant smell due to burning oil products. Classes in schools were cancelled, the council said, and it asked people to stay indoors and to seal doors and windows.
Separately, Ukrainian state oil and gas firm Naftogaz said a Russian strike had targeted one of its facilities in a western region in the 15th deliberate attack on its infrastructure in this month alone.
Russian and Ukrainian officials are expected to hold another round of US-brokered talks on Sunday after meeting last weekend in Abu Dhabi.
Writing on X, Zelenskiy urged Kyiv's allies to step up pressure on Moscow, which has demanded Ukraine give up land that Russian forces have been unable to conquer before it stops fighting.
"We expect the United States, Europe, and other partners not to remain silent about this and to remember that achieving real peace requires pressure precisely on Moscow."
Ukraine is asking partners, particularly the US, for strong security guarantees in the event of a peace deal that would prevent Russia from attacking again.
