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In some of the strongest criticism of the Kremlin's war in Ukraine from a prominent Russian, Mr Tinkov said online that 90 per cent of Russians were "against this war". He also ridiculed Russia's army.
One of Russia's best-known entrepreneurs, he founded the Tinkoff Bank in 2006. He has been based outside Russia in recent years.
Russian President Vladimir Putin sent troops to Ukraine on February 24 to "de-Nazify" the pro-western country.
The conflict has killed thousands of people and displaced more than 12 million in the largest refugee crisis in Europe since the Second World War.
"Waking up with a hangover, the generals realised that they have a [expletive] army," Mr Tinkov, 54, said in a post on Instagram.
"And how will the army be good, if everything else in the country is [expletive] and mired in nepotism, sycophancy and servility?
"I don't see a single beneficiary of this insane war. Innocent people and soldiers are dying."
Switching to English, Mr Tinkov, who stepped down as chairman of Tinkoff Bank in 2020, said: "Dear 'collective West', please give Mr Putin a clear exit to save his face and stop this massacre.
"Please be more rational and humanitarian."
Mr Tinkov, who has had western sanctions imposed on him, posted his statement on the 55th day of Moscow's military campaign, with Russian forces launching a major offensive in the eastern Donbas region.
"Ninety per cent of Russians are against this war," he said.
"Of course there are morons who draw 'Z' but 10 per cent of any country are morons."
Mr Tinkov was referring to the 'Z' drawn on Russian military vehicles that were involved in the Ukraine fight, which has become a symbol of support for the war.
He said Kremlin officials were "in shock" that they and their children will no longer be able to spend their summer holidays on the Mediterranean.
"Businessmen are trying to rescue what's left of their property," Mr Tinkov said.
Russian authorities have tried to muffle dissent over Moscow's invasion of Ukraine, imposing prison terms of up to 15 years for publishing "fake news" about the army.
Tinkoff Bank said it would not comment on Mr Tinkov's "private opinion" as he no longer made decisions on operations of companies under the brand.
"He is not a Tinkoff employee, has not been in Russia for a long time and has been dealing with health issues in recent years," the bank said.