Workers were evacuated after the attacks on logistics centres in Krasnodar and Nevinnomyssk, Wildberries founder and Russia's wealthiest woman Tatyana Kim said earlier on Wednesday.
"There are no words to describe all the feelings and emotions caused by the attacks on ordinary people, on our employees, on us, who are simply doing our jobs," she wrote on Telegram. "But these situations demonstrate the most important thing: we must continue to do what we do for the benefit of people."
In Krasnodar, 10 people were injured in an attack on a warehouse complex, with three in a serious condition, the region's Governor Veniamin Kondratyev said.
He later said that a young woman died of her injuries in hospital.
Five people were hurt in a warehouse complex on the outskirts of Nevinnomyssk, Stavropol Governor Vladimir Vladimirov said.
BBC Verify has analysed footage and confirmed fires in the two locations.
Several hours after the latest attacks, a range of military gear - including body armour and drone components - was widely available on Wildberries' website, a quick search by the BBC showed.
Serhii Kuzan, chairman of the Ukrainian Security and Cooperation Centre, has described Wildberries as a "vital component" of Russian logistics, adding that the firm's website is being used by Russian volunteers to buy military equipment.
"The primary rationale for striking Wildberries' warehouses is to disrupt Russian logistics and the supply of dual-use goods, critical electronics, sanctioned goods and the like to the Russian army and Russian arms manufacturers," Kuzan told the BBC.
"The collateral damage from such strikes could also have a serious impact on the Russian economy, as well as a psychological effect on Russian society and, likely, on continued support for the war."
The Ukrainian strikes have also dealt a serious blow to Russia's small and mid-sized businesses, angering hundreds of sellers whose livelihoods depend on online marketplaces.
Unlike retail giant Amazon, Wildberries and its rival Ozon act almost entirely as marketplaces, connecting independent sellers with buyers across Russia, storing and delivering their goods, and handling payments.
The recent strikes have impacted hundreds of sellers whose livelihoods depend on online marketplaces.
Trader Elena, not her real name, told BBC Russian she had lost clothing she sells in the attacks, which is her only income.
She said that "if there are more strikes, I probably won't manage. It's terrifying to keep loading my goods into what feels like a furnace".
"I am a mother of a disabled child, I've built the business myself", wrote another trader, in post that has gone viral on social media.
"I've lost one million roubles (£9,500; $12,730) and it's just my problem now. I'm out of strength. We're already getting screwed over from every direction as it is," she wrote.
Additional reporting by Paul Brown, BBC Verify, Vitaly Shevchenko, and BBC Russian
