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 15:10 (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.
In the capital US occupation forces opened fire on an Iraqi civilian car in al-Jadida district, causing it to burst into flames. Passengers in the car were too badly burnt to be immediately identified.
Witnesses said the incident occurred after unidentified assailants shot at US troops, who responded by opening fire randomly in many directions.
Aljazeera’s correspondent in Baghdad reported more injuries among US occupation forces during a mortar attack on Karaf Qassim – a camp on the outskirts of Samara.
US officials were unwilling to confirm details when contacted by Aljazeera.net, but two helicopters were seen by locals transporting the casualties out of the area.
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.
"Things are under control after some losses, which we regret"
Abd al-Rahman Mustafa,
governor of Kirkuk
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.
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.