Images posted on social media and analysed by BBC Verify show a Tupolev Tu-22 on fire at Soltsy-2 airbase, south of St Petersburg.
Moscow said that a drone was hit by small-arms fire but managed to "damage" a plane. Ukraine has not commented.
The Tu-22 can travel at twice the speed of sound and has been used extensively by Russia to attack cities in Ukraine.
The Russian Ministry of Defence said in a statement that an attack by a "copter-type UAV" took place at around 10:00 Moscow time (08:00 BST) on Saturday.