Attackers targeted Chubais's armored BMW with explosives and automatic weapons.
A bomb went off shortly after Chubais's vehicle drove past on a highway in a Moscow suburb. A car carrying his bodyguards was following closely behind.
Chubais's car immediately sped away from the scene. Chubais's bodyguards engaged in a gunfight with unidentified men at the roadside. Some reports say the attackers, clad in army fatigues, fled into a nearby forest.
Chubais is a chief architect of Russia's post-Soviet privatization program and currently serves as chief executive of Unified Energy Systems. He remains one of Russia's most controversial public figures.
"[The attack] was performed extremely unprofessionally. The purpose wasn't to kill. In principal, what happened couldn't hurt Chubais."
The reasons for the attack are unclear.
State Duma Speaker Boris Gryzlov has ordered an immediate investigation.
"This should be given special attention. I think the law enforcement agencies will be able to find those who ordered this crime and those who carried it out. A crime was committed, although Anatoly Borisovich [Chubais] survived, thank God. But this was a crime," Gryzlov said.
Pavel Felgenhauer, an independent defense analyst based in Moscow, believes Chubais was attacked, not to kill him, but to send him a message.
"[The attack] was performed extremely unprofessionally. The purpose wasn't to kill. In principal, what happened couldn't hurt Chubais," Felgenhauer said.
Felgenhauer says if someone really wanted to kill Chubais, Russia has enough professional contract killers to do the job.
Felgenhauer says such attacks occur frequently in Russia and are usually interpreted as warnings to business competitors. Felgenhauer says Chubais is involved in many business dealings as the head of Unified Energy Systems, where he is pushing through reforms to introduce market competition.
"Yes, different privatization projects and other things are on the way in UES. It involves big money, different interests," Felgenhauer said.
Aleksei Makarkin, deputy director of the Center for Political Technologies, a Moscow-based think tank, disagrees that the aim of the attack was not to kill Chubais.
"It was a political assassination by definition," Makarkin said. "Chubais is a unique personality who has already for two decades been among the 20 -- if not the 10 -- most influential people in Russia."
Makarkin says being the head of the energy company is a political post. He says Chubais is deeply involved in reforms and that these reforms hinder the interests of many in Russia. Chubais became the chairman of UES in 1998 after he left politics.
Makarkin says Chubais is very unpopular in Russia because of the privatization process he led in the 1990s. Quick privatizations marginalized many in the population, and Chubais is considered by many to be the main culprit behind the resulting poverty. But he doesn't believe these people are behind the attack.
"Those who don't love Chubais because for the privatization process do not put bombs on the road," Makarkin said. "They simply do not know how to do it. He crossed the path of many during these years. It makes no difference which of his enemies hired the killers."
Boris Nemtsov, who served as deputy prime minister while Chubais was in the government, says Chubais has received numerous death threats in recent years.
Chubais said in a statement that he understands quite clearly who organized the assassination attempt. He did not name names, however.
"Everything I have been doing -- in reforming the country's energy sector and uniting democratic forces -- I'll continue to do with double the efforts," Chubais said.