A Russian regional governor said on Thursday that air defences had shot down a drone near the Engels air force base, home to long-range strategic bombers.
Russia says Ukraine has already tried to attack the base twice this month, killing at least six Russian servicemen, although it said there was only slight damage to two aircraft.
The base is located near Saratov, 730 km (450 miles) southeast of Moscow and hundreds of kilometres from the frontlines in Ukraine.
"Air defence systems shot down an unmanned aerial vehicle in the Engels region," Saratov Governor Roman Busargin wrote in a message on Telegram on Thursday.
Falling debris damaged residential property but nobody was injured, he said. Reports had circulated on social media of locals reporting an explosion and hearing air raid sirens.
Reuters was unable to immediately verify the reports.
The Engels base is one of two that host Russia's airborne nuclear forces.
The strikes have raised questions about the effectiveness of Russian air defences, particularly when the frontline is so far away.
There was no immediate comment from Ukraine, which has never publicly claimed responsibility for attacks inside Russia but calls them "karma" for the Russian invasion.
(Reporting by Reuters; Editing by Kevin Liffey)