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2 year oldHe is one of seven oligarchs to be hit with fresh sanctions, including asset freezes and travel bans.
The list also includes billionaires Igor Sechin and Oleg Deripaska, both seen as allies of Vladimir Putin.
Prime Minister Boris Johnson said "there can be no safe havens" for those who have supported the invasion.
"Today's sanctions are the latest step in the UK's unwavering support for the Ukrainian people," Mr Johnson said.
"We will be ruthless in pursuing those who enable the killing of civilians, destruction of hospitals and illegal occupation of sovereign allies."
The government had come under pressure to sanction Mr Abramovich, who said he had made the "difficult decision" to sell Chelsea FC earlier this month.
The football club is among the assets frozen as part of the sanctions against Mr Abramovich and its sale has now been stalled.
But the BBC understands the government would consider allowing Mr Abramovich to apply for a special licence to sell the club, providing he can prove he would not benefit from the sale.
The government said it would issue a special licence that allows fixtures to be fulfilled, staff to be paid and existing ticket holders to attend matches.
However, the club cannot sell any more tickets for games, its merchandise shop will be closed, and it will be unable to buy or sell players on the transfer market.
Mr Abramovich, 55, is alleged to have strong ties to Russian President Vladimir Putin, which he has denied.
The government says Mr Abramovich, who has an estimated net worth of £9.4bn, is "one of the few oligarchs from the 1990s to maintain prominence under Putin".
Mr Abramovich has stakes in steel giant Evraz and Norilsk Nickel. He sold a 73% stake in Russian oil firm Sibneft to state-owned gas titan Gazprom for £9.87bn in 2005.
While the sanctions against him throw Chelsea's future in doubt, ministers sought to reassure the club it would not be "unnecessarily harmed".
In a tweet, Culture Secretary Nadine Dorries said holding those who have "enabled the Putin regime to account" was the priority.
"I know this brings some uncertainty, but the government will work with the league and clubs to keep football being played while ensuring sanctions hit those intended," she wrote.
Chelsea has enjoyed major success since Mr Abramovich bought the club in 2003 for £140m, winning major titles including the Champions League, the Premier League and the FA Cup.
Mr Abramovich has previously said that proceeds of the club's sale would be donated to victims of war.
On Wednesday, there were 20 credible interested parties looking at a potential Chelsea takeover, including British businessman Nick Candy.
The UK and its western allies have been ratcheting up sanctions against individuals and companies linked to President Putin since the invasion of Ukraine was launched on 24 February.
The government said Thursday's sanctions against "seven of Russia's wealthiest and most influential oligarchs" were part of the UK's "efforts to isolate Putin and those around him".
Among those sanctioned was Oleg Deripaska, a leading industrialist who has had links with British politicians.
Once one of the richest men linked to President Putin, Mr Deripaska made billions from his stake in Russia's aluminium industries, including EN+ Group, and has a multi-million pound property portfolio in the UK.
His net worth is now an estimated £2bn, according to the Foreign Office, and he has been subject to US sanctions since 2018.
Unlike other Russian oligarchs, who have remained silent on the war in Ukraine so far, Mr Deripaska has called for "peace as soon as possible" in a tweet.
Igor Sechin is another wealthy businessman who is said to have deep ties to President Putin.
Named Putin's right-hand man by the UK, Mr Sechin worked with the president when he was mayor in St Petersburg in the 1990s.
Igor Sechin is the chief executive of Rosneft, a Russian state oil company, and has been sanctioned by the US and EU.
In its statement, the government said the four others sanctioned included:
Foreign Secretary Liz Truss said the government had targeted the oligarchs to "ramp up the pressure on the Putin regime and choke off funds to his brutal war machine".
She said: "With their close links to Putin they are complicit in his aggression.
"The blood of the Ukrainian people is on their hands. They should hang their heads in shame."
Labour's shadow foreign secretary David Lammy said the sanctions were the "right decision" but "should not have taken the government weeks".
"Too few oligarchs linked to Putin's rogue regime have so far faced sanctions from the UK government," Mr Lammy said.
The government has been accused of moving slower than western allies the US and the EU in its sanctioning of individuals linked to President Putin.
The government's Economic Crime Bill, which is expected to become law later this month, is designed to harden and quicken these sanctions.
The government says the bill will also stop wealthy Russians using the City of London for money laundering and hiding gains linked to organised crime.
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