An Aljazeera correspondent said three people were killed and nine injured, including the cleric Ayat Allah Muhammad Said al-Hakim. Al-Hakim's driver and two bodyguards were reportedly among the dead.
"There was an explosion 800m south of the Imam al-Ali mosque in Najaf at 3.10pm (11:10 GMT) this afternoon," said a US military spokesman on Sunday.
The Imam Ali mosque holds the tomb of Ali, a cousin of the Prophet Muhammad, and is the most sacred Shia site in Iraq.
The Iranian news agency IRNA reported al-Hakim, a senior cleric in Najaf, had suffered a neck injury from the blast, which happened outside his office.
He is the uncle of Ayat Allah Muhammad Baqir al-Hakim, the leader of the Supreme Council for the Islamic Revolution in Iraq (SCIRI) who returned to Iraq in May.
SCIRI is one of the main Shia groups represented on Iraq's
US-appointed governing council.
Ethnic violence flares in north
Elsewhere, Kurds and Turkmen traded accusations on Sunday in the aftermath of ethnic violence that left more than 10 dead in northern Iraq and added to the country's lawlessness.
The Kurdish governor of Kirkuk, a northern city at the heart of Iraq's richest oil reserves, said at least two people were killed in clashes between Kurds and Turkmen on Saturday.
"Things are under control after some losses, which we regret"
Abd al-Rahman Mustafa,
governor of Kirkuk
That violence was ignited by unrest in the nearby town of Tuz Khurmatu, where residents say nine died in violence on Friday.
Abd al-Rahman Mustafa, whose appointment as governor of Kirkuk is resented by many Turkish-speaking Turkmen in the city, said he would investigate accusations that Kurdish police had opened fire unprovoked on protesters.
"Things are under control after some losses, which we regret," he told Reuters at the municipal government building, guarded by local police and US patrols. Traffic flowed normally in the city on Sunday and shops were open.
Both Kurds and Turkmen recount persecution in Kirkuk during the rule of Saddam Hussein, when many were expelled from the city and replaced with Arabs from other parts of the country in an attempt to change Kirkuk's ethnic make-up.
The Turkmen, whose presence in Iraq dates back to Ottoman rule, say they now face oppression by the Kurds, and accuse the Patriotic Union of Kurdistan (PUK) of inciting ethnic violence.
The mayor of Tuz Khurmatu, about 70km south of Kirkuk, said the fighting began when Turkmen accused Kurds of desecrating a Shia shrine.
Turkish newspapers blamed Kurdish "peshmerga" fighters belonging to the PUK for the unrest. Turkey, which wants to suppress Kurdish separatism within its own borders, has expressed concern about growing Kurdish influence in Iraq.
The PUK denied any role in the violence and said "foreign elements" and "elements of the former regime" were under suspicion.