Kyiv's authorities said it seemed all incoming missiles had been destroyed, but debris falling from the air caused some damage in two districts.
One person has been killed and two more wounded in a missile strike on the Black Sea port of Odesa, officials say.
Blasts were also heard in the central-western regions of Vinnytsia, Khmelnytsky and Zhytomyr.
Overall, 29 out of 30 missiles launched by Russia overnight were shot down, Ukraine's Air Force said in a statement.