"As it was climbing after taking off from the Hmeimim airbase, the Russian fighter Su-30SM crashed into the Mediterranean Sea. Two pilots, who fought until the last minute to save the plane, died, according to reports from the scene," the statement said.
The ministry said the plane had not come under fire, adding that "according to preliminary information, the reason for the crash could have been a bird falling into the engine".
The accident brings Russia's official military losses in Syria to 86.
The most recent acknowledged military loss came when a transport plane crashed on landing at the Hmeimim airbase in March, killing all 39 people on board.
But Russian nationals are regularly reported to be serving as paid mercenaries in Syria and taking on dangerous missions that often lead to casualties.
Russia provides the bulk of the Syrian regime's arsenal, which has been used extensively during the war.
Fighting was sparked in 2011 after peaceful protests were brutally suppressed by regime troops leading to mass defections from the Syrian army.
Russia joined the war in 2015, after forces loyal to Bashar al-Assad suffered a series of military defeats against the rebels.
Since Russian airstrikes began, regime forces have managed to push the opposition back to a number of enclaves but the cost has been devastating for civilians.