Brussels said Mr Volozh, who held one-to-one meetings with Putin in 2017 and 2020, had “materially or financially” supported the war against Ukraine.
In 2017, he invited Mr Putin to Yandex’s headquarters in Moscow where he showed him the company’s new self-driving car and AI-based products.
In Thursday’s statement, he said he had been helping “talented Russian engineers” leave the country “to start a new life”, saying he had “reasons to stay silent during this long process”.
The entrepreneur is seeking to downplay his 25 years as chief executive of the Russian business, describing himself as a “Kazakhstan-born” Israeli – and Yandex as “one of the largest internet companies in Europe.”
Yandex is a tech giant in Russia and has been accused of helping the country’s government suppress freedom of speech and enable mass surveillance.
Its products include a Russian-language search engine, a music streaming service and a gaming platform.
Nasdaq officials suspended its shares from trading on the US index in February 2022, immediately after the invasion. Its market cap at the time was $6.6bn (£5.2bn).
A representative of Mr Volozh declined to comment further. Yandex did not respond to a request for comment.
Russia’s recent track record against political and business figures who speak out against Putin’s government or the war in Ukraine has shown no sign of letting up almost 18 months after the invasion started.
Ilya Sachkov, the 37-year-old founder of cyber security company Group-IB, was jailed for 14 years in July after Moscow accused him of passing state secrets to the USA.
His 2021 arrest prompted the exit of Group-IB, once seen as one of Russia’s cutting-edge tech companies, from the country.
Political opponents of Mr Putin have also been thrown in jail for peaceful opposition to his regime.
Vladimir Kara-Murza, an opposition politician and journalist who grew up in north-west London, was sent to a penal colony for 25 years in April.