Governor Dmitry Azarov said in a statement posted on the Telegram messaging app that the Volga river region's Syzran refinery was on fire, but that an attack on the Novokubyshev refinery had been thwarted.
He said workers at both plants had been evacuated, and that there were no casualties.
Unverified footage published online showed what appeared to be a major fire at the Syzran refinery, with emergency services working at the scene.
Ukraine has in recent weeks heavily targeted Russia's oil infrastructure, striking refineries throughout European Russia.
Russia is voting today in three-day presidential elections, with President Vladimir Putin on Friday accusing Ukraine of attempting to sabotage the polls he is certain to win.
(Reporting by Reuters; Writing by Felix Light; Editing by Tom Hogue)
