Both sides blamed the other for destroying the dam.
Unverified videos on social media showed a series of intense explosions around the Kakhovka dam.
Other videos showed water surging through the remains of the dam with bystanders expressing their shock, sometimes in strong language.
The dam, 30 metres tall and 3.2 kilometres long, was built in 1956 on the Dnipro River as part of the Kakhovka hydroelectric power plant.
It holds an 18km cubed reservoir which also supplies water to the Crimean peninsula, annexed by Russia in 2014, and to the Zaporizhzhia nuclear plant, which is also under Russian control.
Ukraine's military said that Russian forces blew up the dam.
"The Kakhovka (dam) was blown up by the Russian occupying forces," the South command of Ukraine's Armed Forces said on Tuesday on its Facebook page.
"The scale of the destruction, the speed and volumes of water, and the likely areas of inundation are being clarified."
Russian news agencies said the dam, controlled by Russian forces, had been destroyed in shelling while a Russian-installed official said it was a terrorist attack - Russian shorthand for an attack by Ukraine.
Reuters was unable to immediately verify the battlefield accounts from either side.
It comes as Russia said it thwarted another major Ukrainian offensive in Donetsk, inflicting heavy losses, while Ukraine hailed progress in fighting in the east, although it was unclear if it marked the start of a long-anticipated Ukrainian counteroffensive.
On Monday, Russia said Ukrainian forces had begun a major offensive at the weekend in the southern part of the Donetsk region, which it had also thwarted.
Ukrainian officials have made no mention of any broad, significant new campaign although, in his nightly address on Monday, Ukrainian President Volodymyr Zelenskiy was enigmatic, hailing "the news we have been waiting for" and forward moves in Bakhmut in Donetsk.
Russian President Vladimir Putin sent troops into Ukraine on February 24 last year in what the Kremlin expected to be a swift operation, but its forces suffered a series of defeats and regrouped in the country's east.
Tens of thousands of Russian troops dug in for the winter, besieging Bakhmut for months and bracing for an expected Ukrainian counterattack to try to cut Russia's so-called land bridge to the Crimean Peninsula.
The latest Russian defence ministry statement said Russian forces had inflicted huge personnel losses on attacking Ukrainian forces and destroyed 28 tanks, including eight Leopard main battle tanks and 109 armoured vehicles.
It said total Ukrainian losses amounted to 1500 troops.
Reuters could not independently verify the reports.
There was no immediate comment from Kyiv about Russia's assertions.
Ukrainian Foreign Minister Dmytro Kuleba told Reuters on Monday Ukraine now had enough weapons for a counteroffensive but declined to comment when asked whether it had begun.
In a promotional video released on Sunday and urging silence in regard to any military actions, Ukraine's defence ministry said: "Plans like silence - the beginning will not be announced."
The success or failure of a counteroffensive, expected to be waged with billions of dollars worth of advanced Western weaponry, is likely to influence the shape of future Western diplomatic and military support for Ukraine.