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Anatoly Chubais has stepped down from his role as an international envoy for President Vladimir Putin, the most senior official to resign since Russia's invasion of Ukraine.
Russian reports said he was currently in Turkey with his wife.
Mr Chubais was given the job of coordinating Russia's sustainable development goals internationally.
After the war began he posted a picture of a murdered opposition figure, in what was seen as a critical gesture.
There was no comment to accompany his Facebook photo of Boris Nemtsov, on the anniversary of his killing in view of the Kremlin. He has also made no comment yet on his resignation.
"Yes it's true Anatoly Borisovich is leaving his post," a source told the Tass news agency, which quoted another source saying he had left Russia as well as resigning as a special representative to President Putin.
Russia has clamped down on criticism of the invasion, which began on 24 February, requiring state-run media to describe it as a "special military operation".
A new law bans the dissemination of "false news" about the war and political journalist Alexander Nevzorov became the most prominent figure yet to be prosecuted, after he posted details on social media about Russia's deadly attack on a maternity hospital in the southern Ukrainian city of Mariupol.
Mr Chubais is best known for his controversial role in helping to reform Russia's economy in the 1990s after the fall of the Soviet Union. The raft of privatisations under President Boris Yeltsin helped create a large number of very wealthy oligarchs.
Since Mr Putin's rise to power he has held a number of jobs, including head of the state technology firm Rusnano for many years.
When he was given the job of special representative for ties with international organisations, officials said he would not be part of the Kremlin staff.