Ukraine did not directly claim responsibility. If it did carry out the attacks, they were the deepest military strikes it has conducted inside the Russian heartland since the start of what Moscow calls "special military operation" on Feb. 24.
One of the targets, the Engels air base near the city of Saratov, houses bomber planes that are part of Russia's strategic nuclear forces.
"The Kyiv regime, in order to disable Russian long-range aircraft, made attempts to strike with Soviet-made unmanned jet aerial vehicles at the military airfields Dyagilevo, in the Ryazan region, and Engels, in the Saratov region," the Russian defence ministry said.
It said the drones, flying at low altitudes, were intercepted by air defences and shot down. The wreckage caused slight damage to two aircraft, it said, and four people were wounded.
The ministry called it a "terrorist act" aimed at disrupting its long-range aviation.
Despite that, it said, Russia responded with a "massive strike on the military control system and related objects of the defences complex, communication centres, energy and military units of Ukraine with high-precision air- and sea-based weapons" in which it said all 17 designated targets were hit.
Ukraine said it shot down more than 60 of over 70 missiles launched by Russia on Monday - the latest in weeks of attacks targeting its critical infrastructure that have cut off power, heat and water to many parts of the country.
Russia's RIA news agency said the three deaths occurred at the air base in Ryazan, 185 km (115 miles) southeast of Moscow.
The other base that was hit was Engels, near the city of Saratov, about 730 km southeast of Moscow. It is one of two strategic bomber bases housing Russia's air-delivered nuclear capability, the other being in Amur region in the Russian Far East.
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.
Saratov is at least 600 km from the nearest Ukrainian-held territory. Russian commentators noted on social media that if Ukraine could strike that far inside Russia, it may also be capable of hitting Moscow.
Kremlin spokesman Dmitry Peskov told reporters at a morning briefing that President Vladimir Putin was aware of the incidents, but declined further comment.
Ukrainian officials acknowledged the incidents on social media with tongue-in-cheek comments.
Presidential adviser Mykhailo Podolyak wrote on Twitter: "If something is launched into other countries' airspace, sooner or later unknown flying objects will return to (their) departure point."
Ukraine has previously demonstrated the ability to strike strategic Russian targets far beyond the 1,100 km-long front lines in the south and eastern Ukraine.
In August, at least seven Russian warplanes were destroyed by explosions at a Russian airbase on the southwest coast of Russian-annexed Crimea.
Ukraine did not publicly claim responsibility for that, or for a spate of explosions at sites such as weapons stores and fuel depots in Russian regions close to the border with Ukraine.
Reuters