The Mi-8 transport helicopter was returning to Hmeimim base in Idlib province after delivering humanitarian aid to Aleppo when it came under attack from the ground on Monday, BBC quotes the Russian ministry as saying.
All five people in the aircraft were killed, according to the Kremlin.
Images shared on social media apparently showed a dead body stripped of clothes and Russian identity documents taken from the helicopter, Reuters reported.
Rebel groups are staging an offensive to break a government siege on rebel-held parts of Aleppo around 25 miles from the reported crash site.
Pro-Syrian government forces on the ground are being supported by heavy air strikes in the same area.