Ukraine has not officially claimed responsibility for the explosions, which were reportedly heard around dawn.
Moscow has said the West may be involved in an alleged Ukrainian attack on a key bridge in Crimea, which took place during the early hours of Monday morning.
Russia’s foreign ministry says Western countries could have colluded in what it called a Ukrainian “terrorist” attack on the Kerch bridge, linking the Black Sea peninsula to mainland Russia.
If drones used in the alleged strike came from the West and if Ukraine's allies were involved in “planning, sponsoring and carrying out this operation” - that would “confirm their complicity", the ministry said on Monday.
Russian officials say two people died in what they initially called an "emergency" on the bridge.
The Russian-installed head of Crimea's parliament Vladimir Konstantinov said Ukraine had committed a "crime" by targeting "civilian" infrastructure, according to state-backed Russian media.
Ukraine has not officially claimed responsibility for the blasts, and Euronews cannot independently verify Russia's claims.
A spokesperson from Russia's foreign ministry said earlier that Ukrainian decisions were taken "with the direct participation of American and British intelligence agencies and politicians".
They did not provide evidence for this claim.
Traffic was halted on the bridge off the coast of southern Ukraine, following reports from locals they heard explosions at dawn.
Crimea govenor Sergei Aksyonov announced the was closed early Monday.
The two people known to have been killed were a mother and father from Russia's Belgorod region going on a family holiday, according to the region's governor Vyacheslav Gladkov.
Writing on Telegram, he said their 14-year-old daughter was also "moderately injured".
"The hardest thing is that her parents died," he added.
The extent of the damage was not immediately clear, though rail traffic on the bridge has since resumed.
Trains are delayed, however, and long traffic jams on the remaining route out of Crimea have been reported.
The 19-km bridge, which was opened in 2018, is a key supply route for Russian forces in southern Ukraine.
It was damaged in October by a truck bomb and required months of repairs before resuming full service.
Crimea was illegally annexed by Russia in 2014, soon after Ukraine deposed its pro-Moscow president Viktor Yanukovych in the Maidan revolution.