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.
It stated the location as “a military airfield in the Novgorod region”, where Soltsy-2 is situated.
“The UAV was detected by the airfield’s observation outpost and was hit with small-arms fire,” the ministry said.
“One airplane was damaged; there were no casualties as a result of the terrorist act.”
The statement also said a fire which broke out in the airfield parking lot was quickly extinguished.
However, images posted on the social media platform Telegram showed a large fire engulfing a jet with the distinctive nose cone of the Tu-22. BBC Verify analysed the images and believes them to be credible.
While the destruction of a single aircraft will have little effect on the potency of Moscow’s current 60-strong fleet, the operation highlights Kyiv’s growing ability to strike targets deep inside Russian territory.
Kyiv has over recent months launched dozens of fixed-wing unmanned aircraft to attack Moscow, a journey of several hundred miles. Soltsy-2 is around 400 miles (650km) from the Ukraine border.
However, the Russian MoD’s description of the drone as a “copter-type UAV” suggests a cheap, commercially available device launched at short range.
The Tu-22 is a Cold War-era, swing-wing supersonic bomber, codenamed “Backfire” by Nato, which has been used extensively in attacks on Ukrainian cities.
Modern versions such as the Tu-22M3 can reach speeds of Mach 2 (2,300km/h or 1,430mp/h) and can carry up to 24,000kg of weapons, including “dumb bombs” and homing missiles.
They have been used in conflicts in Syria, Chechnya, and Georgia and most recently in Ukraine.
According to prosecutors in Kyiv, 30 people were killed when a Tu-22-launched missile hit a block of flats in Dnipro in January.
They said Russia’s 52nd Guards Bomber Aviation Regiment carried out the attack. The regiment is based at Soltsy-2.
BBC Verify confirmed the location of the Ukrainian drone attack on Soltsy-2 by comparing visual clues – such as the appearance of aircraft and bays – to historical satellite images of the airbase.
The weather conditions at the time – wet and overcast – also matched the weather in the images, as well as other witness photos of the incident.
The remnants of the aircraft visible in the footage are consistent with that of a Tu-22M3.
Historical satellite imagery analysed by BBC Verify shows that aircraft of this kind were stationed at the base.
On Monday, a spokesperson for Ukraine’s defence intelligence service said another military aircraft had been damaged in a drone attack in Russia’s Kaluga region.
Russian media also reported the attack, but denied there had been any damage.