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2 year oldRussian officials said a fire triggered the blasts in the Dzhankoi area - before later blaming "sabotage".
A separate fire broke out at power substation and a railway was damaged.
A string of blasts last week destroyed Russian warplanes at a Black Sea base on the Crimean coast.
Ukraine has never publicly admitted that attack - but presidential office adviser Mykhailo Podolyak described the latest incident as "demilitarisation in action", indicating that the explosions were not accidental.
A Crimean Tatar leader, Refat Chubarov, called the explosions a "hit" that could be heard "far across the steppe".
Russia's defence ministry said the fire broke out at a temporary ammunition storage site near the village of Maiske (or Mayskoye in Russian) at around 06:15 Moscow time (03:15 GMT) and that the cause was being investigated.
The defence ministry in Moscow said there had been no "serious" casualties, but Russian-appointed regional head Sergei Aksyonov visited the site and said 2,000 people had been moved from a nearby village and two people had been wounded.
"One man has a shrapnel wound, and one was crushed by a wall. Their lives are not in danger, fortunately," he said.
Crimea was seized from Ukraine and then annexed by Russia in early 2014, and when Russian forces unleashed a new invasion in February they used their bases on the peninsula to capture large swathes of southern Ukraine.
Russian occupation has stretched across two southern regions in particular, Kherson and Zaporizhzhia, and Ukraine has vowed to launch a counter-offensive to recapture areas under Russian control.
After the Russian air base at Saky was hit last Tuesday, satellite images revealed significant damage, with at least eight warplanes destroyed. Although Russia said that incident was also accidental, there was little doubt the base had come under Ukrainian attack due to the precise nature of the destruction.
The UK Ministry of Defence said the blasts had "significantly degraded" the aviation capability of the Russian navy's Black Sea fleet.
The latest blasts at an ammunition depot are reminiscent of a string of recent attacks behind Russian lines in eastern Ukraine.
Since June, Ukrainian forces have used US Himars multiple rocket launchers to hit as many as 50 arms stores, according to the defence minister. Bridges in the south have also been hit, jeopardising vital supply lines from Crimea to Kherson.
The apparent ability of Ukraine's military to reach so far behind enemy lines is of significant embarrassment to the Russians. The explosions at Saky were visible from nearby beaches and videos posted afterwards on social media showed streams of tourists leaving Crimea, across a bridge built across the Kerch Strait after the Russian annexation.