Shares in embattled oil firm Yukos have nosedived amid increasing concerns about its ability to avoid bankruptcy.
Mr Nevzlin is estimated to have a personal fortune of $2bn
Yukos lost a fifth of its stock market value on Monday, and its rouble-denominated shares were temporarily suspended due to the sharp fall.
A Moscow court earlier issued an arrest warrant for a major Yukos shareholder, accusing him of involvement in murder.
Leonid Nevzlin, who is living in Israel, is accused of ordering the killing of a married couple in 2002.
He also is facing charges of attempted murder.
A lawyer for Mr Nevzlin said the charges would be challenged.
Yukos shares fell 22% to $4.20 in Moscow, leading some analysts to argue that the company's chances of avoiding financial collapse were increasingly slim.
Yukos has lost half its market value since last Wednesday, the day after state bailiffs said they would sell off the firm's main production unit - Yuganskneftegaz - in order to help pay the company's $7bn tax bill.
Yukos executives have expressed fears that the unit, which accounts for 60% of its oil output, could be sold for as little as $1.75bn. Yukos values it at $30bn.
Analysts said that investors who had bought into the company in the hope that it may reach a settlement with the government in its tax dispute were now selling out.
"We are getting into the first signs of market surrendering," said Kakha Kiknavelidze, a leading analyst.
"It looks like surrender," another said. "A lack of liquidity is playing against Yukos."
Mr Nevzlin fled to Israel shortly before the arrest of the oil giant's former boss, Mikhail Khodorkovsky.
Mr Khodorkovsky is on trial on charges of fraud and tax evasion.
The court in Moscow's Basmanny district said the alleged killing and attempted murders were organised by Yukos's former head of security, Alexei Pichugin, on the orders of Mr Nevzlin, Interfax reported.
Mr Nevzlin's lawyer, Dmitry Kharitonov, said he was studying the court order and would "launch a protest against it by all means", Russian news agency Itar-Tass reported.
Mr Nevzlin is estimated to have a personal fortune of $2bn (£1.1bn), according to Forbes magazine.
He arrived in Israel last autumn as legal proceedings against Yukos were intensifying and was granted Israeli citizenship.
However, authorities in Israel have previously said that Mr Nevzlin's new citizenship would not automatically prevent his extradition to Russia.
The on-running case against Mr Khodorkovsky is widely seen as a Kremlin-inspired drive to punish Russia's richest man for funding opposition political parties and to deter him from further political activity.
Yukos has warned it could be driven into bankruptcy after a court ordered it to pay a $3.4bn tax bill.