Odesa Governor Oleh Kiper said the attack damaged residential buildings in the city’s historic centre and struck both a nursery and an inclusive education centre. Among the injured were a pregnant woman and a 17-year-old girl.
The attack follows a deadly night in Kyiv, where at least 14 people were killed and nearly 100 injured as missiles and drones hit the capital.
Russia has stepped up its aerial assaults in recent weeks, following a Ukrainian operation that targeted Russian air bases.
Ukrainian President Volodymyr Zelenskyy said peace talks have seen little movement, aside from a planned prisoner exchange.