Libya's deputy interior minister Wanis al-Sharif told AFP: "One American official was killed and another injured in the hand. The other staff members were evacuated and are safe and sound."
He could not say if the dead man was a diplomat.
"Demonstrators attacked the US consulate in Benghazi. They fired shots in the air before entering the building," said Sharif, who is in charge of the country's eastern region.
Abdelmonoem al-Horr, spokesman for the Libyan interior ministry's security commission, said rocket-propelled grenades were fired at the consulate from a nearby farm.
Security forces and the interior ministry were trying to contain the situation, he added.
Witnesses said the attackers ripped up an American flag, then looted the consulate before setting it on fire on the eleventh anniversary of the September 11 attacks.
"Dozens of demonstrators attacked the consulate and set fire to it," said a Benghazi resident, who only gave his name as Omar, adding that he had seen the flames and heard shots in the vicinity.
Another Libyan witness said armed men had closed the streets leading up to the consulate, among them ultra-conservative Salafists.
The violent protest was strongly condemned by Libya's General National Congress, which in a statement expressed "outrage at the unfortunate attack against the American consulate in Benghazi."
In Washington, state department spokeswoman Victoria Nuland said: "We condemn in strongest terms this attack on our diplomatic mission."
US officials were working with the Libyans to secure the compound, Nuland said, adding that the earlier protest against the US embassy in Cairo, in which demonstrators scaled the walls, had now ended.
The Libyan incident came after thousands of Egyptian demonstrators tore down the Stars and Stripes at the US embassy in Cairo and replaced it with a black Islamic flag, similar to one adopted by several militant groups.
Nearly 3,000 demonstrators, most of them hardline Islamist supporters of the Salafist movement, gathered at the embassy in protest over a film deemed offensive to the Prophet Mohammed which was produced in the United States.
A dozen men scaled the embassy walls and one of them tore down the US flag, replacing it with a black one inscribed with the Muslim profession of faith: "There is no God but God and Mohammed is the prophet of God."
Egyptian police intervened without resort to force and persuaded the trespassers to come down. The crowd then largely dispersed leaving just a few hundred protesters outside the US mission, an AFP correspondent reported.
The Wall Street Journal reported that the film, "Innocence of Muslims," was made by Israeli-American Sam Bacile, a 52-year-old real-estate developer from southern California who says Islam is a hateful religion.
"Islam is a cancer," Bacile told the newspaper.
The film is being promoted by controversial Florida pastor Terry Jones, who has drawn protests in the past for burning the Koran and vehemently opposing the construction of a mosque near Ground Zero in New York.
Arab League deputy secretary general, Ahmed Ben Helli, has condemned the film saying it "contained insults against the prophet Mohammed" and "was denounced by Christians and Muslims" across the Arab world.
Tuesday's protests came on the eleventh anniversary of the attacks of September 11, 2001, when US cities were targeted by hijacked planes.
Egyptian activist Wael Ghoneim wrote on his Facebook page that "attacking the US embassy on September 11 and raising flags linked to Al-Qaeda will not be understood by the American public as a protest over the film about the prophet.
"Instead, it will be received as a celebration of the crime that took place on September 11," he said.
Benghazi, a stronghold of Islamist extremists and cradle of the revolution that saw strongman Moamer Kadhafi captured and killed last year, has seen a wave of violence in recent months, including attacks on Western targets, bombings of military buildings and the killings of army and security officers.
Interior Minister Fawzi Abdelali has warned that Islamists amount to a "major force" in Libya both in terms of numbers and arms.