Ukraine’s emergency service said most of the outages were recorded on Monday evening and urgent repair works were underway.
It did not disclose how many homes or people were left without power.
But the service said its teams had rescued 322 people from 148 vehicles on Monday in the Black Sea region of Odessa alone.
They also pulled out 42 ambulances and two passenger buses from snowdrifts that have been hitting the eastern region of Kharkiv since the weekend.
The weather forecast centre predicted more clement weather in the days ahead. But night temperatures in the Ukrainian capital Kiev were still expected to plunge to minus 15 degrees Celsius (5 degrees Farenheit) into the start of next week.