Police said the blast occurred on Thursday between an ancient cemetery and the Imam Ali shrine, one of the most sacred Shia sites. The mosque was not damaged.
“When the black Opel car exploded, I could only see human flesh flying in the air,” said Mahmoud Mohsin, 38, a drinks seller, who was being treated in hospital for head wounds.
Hospital officials said the bomb killed 13 people and wounded about 40 others, but police put the death toll at 15. A Reuters correspondent saw 10 bodies and body parts on the ground.
Najaf is 160km south of Baghdad.
In February, the bombing of another Shia shrine in the town of Samarra touched off reprisals and pushed Iraq to the edge of a full-blown sectarian conflict.
Thursday’s blast came amid growing calls for Ibrahim al-Jaafari, the interim prime minister, to step down in order to boost efforts to form a government four months after elections.
Frustration among Iraqis exploded amid the carnage at the scene of the blast, where a man stood clutching a severed hand.
“Where is the government? Where is Jaafari? Where is Sistani?,” he yelled, referring to Grand Ayatollah Ali al-Sistani, the Shia cleric whose calls for moderation are credited with keeping Iraq from reaching the point of no return.
“Where is the government? Where is Jaafari? Where is Sistani?”
Kurdish and Sunni leaders refuse to work with al-Jaafari and senior officials in his Shia Alliance say he should step aside. However, al-Jaafari keeps deflecting criticism that he failed to improve security during his year as interim prime minister.
Speaking at a live conference on state television, al-Jaafari repeated what he has been saying all along.
“I have no hesitation in stepping down from my position. If my [the Iraqi] people decide that, I will respond,” he said.
The push for a new government has exposed sharp differences within the Shia majority, divided in parties backed by rival militias.
Al-Jaafari’s main supporter in the alliance is Moqtada al-Sadr, a radical cleric who has led two bloody uprisings against US and Iraqi troops.
The United States and Britain told Iraqi leaders this week that the political vacuum left by their bickering would only fuel violence.