Both sides blamed the other for destroying the dam.
Unverified videos on social media show water surging through the remains of the dam with water levels racing up by metres in a matter of hours on Tuesday.
The Nova Kakhovka dam, 30 metres tall and 3.2 kilometres long, was built in 1956 and supplies water to the Crimean peninsula, annexed by Russia in 2014.
It is also linked to the Zaporizhzhia nuclear plant, which is also under Russian control and which gets cooling water from the reservoir.
The International Atomic Energy Agency (IAEA) said there was no immediate nuclear safety risk at the plant due to the dam failure but that it was monitoring the situation closely. The head of the plant also said there was no current threat to the station.
A Russian-installed official in the town of Nova Kakhovka said on Tuesday residents of around 300 houses had been evacuated.
Ukrainian Prime Minister Denys Shmyhal said up to 80 settlements were at risk of flooding.
The Kakhovka Hydroelectric Power Plant has been "totally destroyed" and cannot be restored after a detonation inside the engine room, Ukraine's state hydroelectric company said.
Ukrainian President Volodymyr Zelenskiy blamed Russia for the damage.
"The destruction of the Kakhovka hydroelectric power plant dam only confirms for the whole world that they must be expelled from every corner of Ukrainian land," Zelenskiy wrote on the Telegram messaging app.
Ukraine's military said Russian forces blew up the dam.
Russian-installed officials in Kherson said Ukraine struck the dam at 11pm on Monday GMT several times, destroying the hydraulic valves of the hydroelectric power station, but said the dam was not totally destroyed.
"We ask all residents of coastal settlements to be ready for evacuation," the Russian-controlled region said. "Emergency and special services of the region are in full readiness and will provide all necessary assistance."
Reuters was unable to immediately verify the battlefield accounts from either side.
It was not immediately clear how the flood waters would affect Ukraine's long planned counter-offensive against Russian forces who are dug in across southern and eastern Ukraine.
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