The depot in the Tambov region southeast of Moscow, which is several hundred kilometres from the Ukrainian border, was previously hit on July 18 when seven people were killed.
That attack heralded the start of Ukraine's aerial campaign that has delivered repeated blows to Russian e-commerce giant Wildberries.
The company's size and commercial importance have brought comparisons with Amazon.
Ukraine's cutting-edge drone capabilities developed since Russia's February 2022 invasion have allowed it to hit dozens of Wildberries facilities across Russia in recent weeks.
Ukraine says goods sold by the company include equipment and technical components that are used by the Russian military.
The attacks have also served Ukraine's war goals by unsettling Russians living far from the front line and hurting the Russian economy.
Ukraine has also targeted oil facilities that are the backbone of the economy in Russia, which is one of the world's largest energy producers.
Ukraine's General Staff said its forces struck a Lukoil refinery in Kstovo, in Russia's Nizhny Novgorod region, overnight.
The facility, which has an annual processing capacity of about 125 million barrels, was on fire after the attack, a General Staff statement said.
Nizhny Novgorod has repeatedly been targeted by Ukraine.
Local governor Gleb Nikitin confirmed the attack and said an unspecified "industrial facility" sustained damage, without providing further details.
The relentless barrages prompted Russian President Vladimir Putin to decree on Monday that the state can temporarily seize control of critical infrastructure facilities if private owners do not protect them from Ukrainian drone attacks or do not rebuild them after the strikes.
Analysts said the move aimed to compel companies to pay for their own security and bring damaged assets back into service, despite the financial cost.
Russia has targeted Ukraine with ballistic and cruise missiles, powerful glide bombs and jet-powered drones, killing thousands of civilians.
A woman and a four-year-old child were killed in a Russian strike on a residential building in the northern Chernihiv region, emergency services said on Wednesday.
Ukraine has been firing hundreds of drones at Russia almost nightly, hoping to overwhelm air defences.
The Russian defence ministry said its forces overnight shot down 426 Ukrainian drones over 15 Russian regions and illegally annexed Crimea.
Ukraine struck Russian oil facilities, airfields, logistics and infrastructure, Ukrainian President Volodymyr Zelenskiy said in a social media post on Wednesday, referring to attacks in the previous 24 hours.
He did not provide details of the targets.
Wildberries confirmed the overnight attack and a fire at its depot in the Tambov region and said the facility was evacuated, but it did not elaborate on the extent of the damage.
Tambov's governor Yevgeny Pervyshov said that the fire completely destroyed the logistical centre and injured two people.
Elsewhere, two people were killed and two others were wounded in Russia's Lipetsk region, south of Moscow, after a drone fell on a house, setting it ablaze, regional governor Igor Artamonov said.
