Seventy-three people were injured with 40 in hospital including four in intensive care, Valentyn Reznichenko, governor of the Dnipropetrovsk region in central eastern Ukraine, wrote at 7:25 a.m. local time (0525 GMT) on the Telegram messaging app.
"The rescue operation is ongoing. The fate of more than 40 people remain unknown," Mr Reznichenko said, adding that the attack had destroyed 72 apartments and damaged more than 230.
But Ukrainian commanders said ground forces were fighting back, using air defences to engage incoming missiles.
Many parts of Ukraine are now under an emergency blackout after missiles struck power infrastructure in several cities.
In Dnipro, central Ukraine, photos and video showed a gaping hole in a nine-storey residential tower block. Smoke billowed out of the ruins as firemen dashed across a destroyed urban park carrying equipment to douse flames.
Rubble was strewn across the ground. Balconies attached to apartments had collapsed on top of one another like a deck of cards.
Kyrylo Timoshenko, the Dnipro region head, said that at least seven children had been left seriously wounded in the attack.
"The youngest is three," he said, adding a nine-year-old had been seriously wounded.
"There are still people under the ruins of the destroyed building. The rescue operation is ongoing. At least one stairwell is gone. Under the rubble there are people who were at home for the holiday."
German Galushchenko, Ukraine’s energy minister, said that there would be power cuts across several regions after the attacks.
"The coming days will be difficult," he wrote on Facebook.