The Russian defense ministry said in a statement three air force personnel had been killed in the incident but no planes were damaged.
However, Russian and Ukrainian social media accounts said a number of planes had been destroyed. Reuters was not able to independently verify those reports.
The attack on the Engels air base - located near the city of Saratov, about 730 km southeast of Moscow and hundreds of kilometers from the frontlines in Ukraine - was the second this month.
It was previously hit on Dec. 5 in what Russia said were Ukrainian drone attacks on two Russian air bases that day.
The air base is one of two strategic bomber bases housing Russia's air-delivered nuclear capability. There was no comment from Kyiv, which has never publicly claimed responsibility for attacks inside Russia.
"A Ukrainian unmanned aerial vehicle (drone) was shot down at low altitude while approaching the Engels military airfield in the Saratov region," the Russian defense ministry statement said.
Three Russian servicemen were killed by falling drone wreckage, it said.
Russia has 60 to 70 strategic bomber planes of two types - the Tu-95MS Bear and the Tu-160 Blackjack. Both are capable of carrying nuclear bombs and nuclear-armed cruise missiles as well as conventional munitions.
Moscow has used its air force to fire cruise missiles in attacks that Kyiv has said amount to war crimes.