Tatarstan regional leader Rustam Minnikhanov said the drones caused “no serious” damage to infrastructure in either location and that production operations were unaffected.
However, Ukraine’s military intelligence said the strike in Yelabuga “caused significant destruction of production facilities”.
Shortly after the attacks, a video circulated online purporting to show a light aircraft – thought to have been modified to fly unmanned – descending onto a building in Yelabuga before exploding, sending a fireball into the air.
On Tuesday morning, drones were also spotted in the Lipetsk region south of Moscow and an air raid alert was introduced, local authorities said.
For several months now, Kyiv has been ramping up its drone attacks on Russian territory.
Ukraine has warned repeatedly that its army is facing severe ammunition shortages, but has set a target of producing a million drones domestically this year.
Earlier this year, Ukraine was reportedly able to hit a major gas export terminal near the city of St Petersburg, 1,250km (775 miles) from the Ukraine-Russia border.
