One of the objects hit was a repair and production facility, Ukraine's national grid operator Ukrenergo said on the Telegram messaging app.
"The damage did not cause any failures in the main network," Ukrenergo added.
It was not immediately clear what other type of facility had come under attack but it was connected to another energy operator.
In a separate statement, the energy ministry said repair crews were working to restore power supplies for domestic consumers and the railway that were cut as a result of the attack.
Russia probably used an X-59 missile, the regional governor Andriy Raikovych said at a briefing.
"Ordinary working people were injured ... One worker, unfortunately, died. A simple car mechanic," he said.
At least seven people were wounded, official data showed. Raikovych added on the Telegram messaging app that all those hurt had suffered shrapnel wounds.
Russia has stepped up attacks on Ukraine around the turn of the year, launching hundreds of missiles of different types and "Shahed" drones since Dec. 29.
(Reporting by Olena Harmash and Yuliia DysaEditing by Mark Potter and Gareth Jones)
