The blasts engulfed an ammunition depot at a military base in the north of the Crimean peninsula, disrupting trains and forcing the evacuation of 2,000 people from a nearby village, according to Russian officials and news agencies.
Plumes of smoke were later seen at a second Russian military base in central Crimea, Russia's Kommersant newspaper said, while blasts hit another facility in the west last week.
Ukraine has not officially confirmed or denied responsibility for explosions in Crimea, though its officials have openly cheered incidents in territory that, until last week, appeared safe in Moscow's grip beyond range of attack.
Ukrainian presidential adviser Mykhailo Podolyak and chief of staff Andriy Yermak both exulted on social media at "demilitarization": an apparent mocking reference to the word Russia uses to justify its invasion.
"Operation 'demilitarization' in the precise style of the Armed Forces of Ukraine will continue until the complete de-occupation of Ukraine's territories. Our soldiers are the best sponsors of a good mood," Yermak wrote on Telegram.
Russia's defense ministry said the explosions at the ammunition depot were "a result of sabotage."
In Tuesday's blasts, an electricity substation also caught fire, according to footage on Russian state TV. Seven trains were delayed and rail traffic on part of the line in northern Crimea had been suspended, Russia's RIA news agency said.
The explosions raised the prospect of new dynamics in the six-month-old war if Ukraine now has capability to strike deeper into Russian territory or pro-Kyiv groups are having success with guerrilla-style attacks.
Russia has used Crimea, which it annexed from Ukraine in 2014, to reinforce its troops fighting in other parts of Ukraine with military hardware, a process Ukraine is keen to disrupt ahead of a potential counter-offensive in southern Ukraine.
Kyiv has never accepted Russia's 2014 annexation of Crimea, nor has the West. There has been speculation that if Ukraine's forces get the chance, they may seek to narrow Russia's hold on that peninsula, or, push it out entirely.
However others say that Russia historically has considered Crimea its own, despite it being handed to Ukraine decades ago. And because of that, an attempt to eject Russia may prompt Moscow to "double down" and increase its aggression there and elsewhere in Ukraine.