An Iraqi Sunni insurgent group said it had carried out the attack, the bloodiest since July 18, when 59 people were killed by a suicide bomb in nearby Kufa.
That bombing was claimed by al-Qaeda, which has attacked Shi'ites in a bid to inflame sectarian passions and trigger full-scale civil war and the Najaf attack appears to have had the same objective.
"God enabled your brothers of the Jamaat Jund al-Sahaba (Soldiers of the Prophet's Companions) to carry out an operation which took the lives of at least 30 rejectionists (Shi'ites), including police," said a statement posted on a main Islamic web site.
The Najaf bomber blew himself up at a police commando checkpoint on his way to the Imam Ali shrine. The defence ministry said 35 were killed and 122 injured.
Ambulances drove through the streets of Najaf appealing for blood donations as the scale of the carnage became clear.
The dead, marked with numbered white labels on their foreheads, included both police and civilians.
Prime Minister condemns attack
Despite a number of horrific attacks over the years since the US-led invasion Najaf has been stable compared to other parts of Iraq, where a Sunni Arab insurgency is aimed at toppling the government of Prime Minister Nuri al-Maliki.
Mr Maliki issued a statement condemning the bombing and blaming loyalists from the regime of former Iraqi leader Saddam Hussein.
"Such brutal massacres reveal the aggressive nature of terrorists, from the Takfirists and Saddamists, who are striving to fuel the sectarian sedition among the Iraqi people," Mr Maliki said.
The US has boosted its troop levels in Baghdad, some 160 kilometres to the north, to try to ease inter-communal bloodshed tearing the capital apart and build confidence in the Shi'ite-led government in power since May.
In southern Baghdad six people were killed by a bomb in a restaurant, while three police died in fighting with gunmen in the nearby district of Um al-Maalif.
A mortar bomb landed on a restaurant on the northern edge of Baghdad, killing at least three people and wounding five.
About 6,000 additional Iraqi forces and 3,500 US soldiers from the 172nd Striker Brigade combat team are being deployed in the Baghdad area.
They are expected to start systematically trying to clear neighbourhoods of militants and insurgents.
More than 1,800 bodies were brought to the Baghdad morgue in July, the largest monthly toll since the aftermath of the bombing of the Shi'ite Golden Mosque of Samarra in February, which triggered a wave of sectarian killing.