The Il-76 transport aircraft were damaged after drones hit an airport in the western Pskov region, located 660km north of the Ukrainian frontier and near the borders of Estonia and Latvia.
Two of the military aircraft "burst into flames" after the attack, Tass news agency reported, and images from the city showed fire rising high into the night sky.
All civilian flights to and from the airport were cancelled on Wednesday so that the damage could be assessed during daylight, Pskov regional governor Mikhail Vedernikov said.
"According to initial assessments, nothing serious has occurred but it is hard to determine that at night. If everything is in order, the airport will resume normal operations on Thursday," he said, adding there were no civilian injuries.
According to the defence ministry, more drones were shot down over Oryol, Bryansk, Ryazan, Kaluga and the Moscow region surrounding the Russian capital.
The airspace around Moscow's Vnukovo airport was shut down briefly for the night following the strikes, while flights at Domodedovo and Sheremetyevo airports were delayed.
Footage shared by the governor showed smoke billowing over the city of Pskov and a large blaze. Unconfirmed media reports said between 10 and 20 drones could have attacked the airport.
Russia has accused Ukraine of steadily escalating its drone attacks on Russian soil and Russian-occupied territory in recent weeks.
Ukraine typically does not comment on who is behind attacks on Russian territory, although officials have publicly expressed satisfaction over them.
Moscow retaliated on Wednesday by launching a "massive combined attack" on the Ukrainian capital using drones and missiles, that killed two people and injured another.
Sergei Popko, the head of the military administration in Kyiv, said Russia launched Shahed drones at the city from various directions and then targeted the capital with missiles from Tu-95MS strategic aircraft.
He said more than 20 targets had been brought down by Ukraine's air defences.
The deaths and injuries occurred when debris fell on a commercial building in the Shevchenkivskyi district, Mr Popko said.
Explosions in Ukraine were also reported in the southern city of Odesa and the Cherkasy region.
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