The incursion was followed by a Russian attack on Kyiv, which officials have said killed two people.
Drones hit an airport in Russia's western Pskov region - near the border with Estonia and Latvia - overnight on Tuesday, triggering a large fire.
Further drones were shot down over Oryol, Bryansk, Ryazan, Kaluga and the region surrounding Russia's capital, Moscow, according to the country's Defence Ministry.
Ukraine has not claimed responsibility for the attacks.
Pskov regional Governor Mikhail Vedernikov ordered all flights to and from the airport in the region's namesake capital to be cancelled on Wednesday, to allow authorities to assess the damage.
Russia's Tass news agency said four l-76 transport aircraft were damaged in the attack.
Footage and images posted on social media showed smoke billowing over the city of Pskov, but Governor Vedernikov said there were no casualties.
Responding to the strike, three of Russia's main airports - Sheremetyevo, Vnukovo and Domodedovo - temporarily suspended all incoming and outgoing flights.
Russian fuel depots and air fields have been a frequent target of drone attacks in recent months - something which Moscow has blamed Ukraine for.
In Kyiv, meanwhile, two people were killed by falling debris, after Russia launched a missile and drone attack on the Ukrainian capital.
The head of Ukraine's military administration, Sergei Popko, wrote on Telegram that the deaths occurred in the Shevchenkivskyi district, in the early hours of Wednesday.
He said the attack was the biggest Russia has launched at Kyiv since Spring.
Ukraine's Air Force said it destroyed 28 cruise missiles and 15 of the Iranian-made Shahed drones involved in the attack.
Want a quick, expert briefing on the biggest stories of the day? Listen to What You Need To Know...