At least 11 people were killed in missile attacks overnight in Ukraine's Dnipropetrovsk region not far from the Russia-occupied Zaporizhzhya nuclear plant, the local military said on Wednesday.

"A tragic night in the Nikopol area the Russian army killed 11 people and injured 13," the head of the Dnipropetrovsk military administration Valentyn Reznichenko said in a Telegram post.

Both of the affected areas are on the opposite bank of the Dnipro River to the Zaporizhzhya nuclear plant, which has been shelled several times in recent days, reports dpa news agency.

The small town of Marhanets was worst hit, with 20 multi-storey buildings damaged including two schools, a dormitory and a cultural centre, Reznichenko said.

Ten people were killed in the town and 11 others injured, seven of them seriously, he said.

In another village close to Nikopol city, another woman died in her home as a result of the attack and a couple was injured.

The two villages are on the north bank of the Dnipro River's Kakhovka reservoir.

On the southern side less than 20 km away is the nuclear plant that has come under fire, sparking international safety fears.

Ukraine and Russia both accuse each other of being behind the attacks.