The Russian military accused Kyiv of using US- and British-supplied missiles and promised the strikes would "not go unanswered".
The barrage forced schools in the southwestern Saratov region to close, while at least nine airports in central and western Russia temporarily halted traffic, according to Russian officials.
Moscow and Kyiv have upped strikes on one another ahead of US President-elect Donald Trump's inauguration next week, as both sides seek to gain the upper hand in potential negotiations aimed at settling the nearly three-year war.
There were explosions at "chemical plants, oil refineries and warehouses" in Russia overnight, a source in Ukraine's SBU security services told AFP, saying Kyiv had hit "Russian military-industrial complex" sites.
Among the targets hit early on Tuesday were chemical plants in the western regions of Tula and Bryansk, the source added.
In the Saratov region, more than 600 kilometres (372 miles) southeast of Moscow, Kyiv struck an oil refinery and an arms depot, the SBU source said.
Regional governor Roman Busargin said the scale of the attack was "massive".
Schools in the cities of Saratov and Engels will hold classes online on Tuesday because of the attacks, he added.
Firefighters had only the day before managed to put out a blaze at an oil depot in the city of Engels, which was hit by a Ukrainian drone strike on January 8.
In the energy-rich region of Tatarstan, a drone struck a gas storage tank, sending flames and thick smoke billowing toward the sky near the city of Kazan, according to media and the regional government.
Tatarstan local media said a liquefied gas storage base was hit, and published images showing flames and black smoke.
- 'Painful strikes' -
Russia's defence ministry said it shot down six US-supplied ATACMS missiles and six British Storm Shadow cruise missiles that Ukraine had fired at the Bryansk border region.
Ukraine's army had earlier claimed a "successful" missile hit on a chemical plant in the region which makes rocket fuel and explosives for Russia's army.
"Drones successfully distracted Russian air defences, paving the way for missiles that hit the main targets," the Ukrainian military's Unmanned Systems Forces said, confirming a hit on a plant near the town of Seltso, more than 100 kilometres from the border.
Ukraine regularly targets military and energy sites in Russia, part of what it calls "fair" retaliation for Russia's repeated barrages of its energy grid since Moscow invaded in February 2022.
"Each damaged ammunition depot, oil refinery, oil depot or chemical plant is a painful blow to Russia's ability to wage war in Ukraine," the SBU source said.
One Ukrainian blogger, who goes by the name of Nikolayevski Vanyok, said on Telegram that the overnight barrage on Russia was "probably one of the most effective" of the war, reaching places "that usually don't get many strikes".
The Ukrainian air force said separately that its air defence systems had downed 58 Iranian-designed drones launched by Russia, while another 21 were destroyed with electronic interference systems or crashed.
A Ukrainian official in the Kharkiv region meanwhile said on Tuesday morning that a 52-year-old resident of the town of Kozachya Lopan had been killed by Russian artillery fire.
The overnight Ukrainian attacks come at a difficult moment for Kyiv's forces along the front line, particularly in the eastern Donetsk region.
City authorities in Pokrovsk, Russia's main target in the region, repeated a call on Tuesday for remaining residents to flee the town, where around 60,000 people lived before Russia invaded in February 2022.
Moscow said on Tuesday it had re-captured two Ukrainian villages in the eastern Donetsk region -- Neskuchne and Terny -- that Kyiv had wrested back from Russian control earlier in the conflict, symbolic blows for Kyiv's struggling army.
Fighting has been intense in the weeks ahead of Trump's inauguration on January 20.
The US Republican has said he wants to end the conflict within "24 hours" of taking office, sparking fears in Ukraine it will be forced to make major territorial concessions in exchange for peace.
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