A police officer said the blast occurred when a car that had been waiting in line to enter the zone, which houses the interim Iraqi government and foreign embassies, exploded as it drove up to a checkpoint.
Several other vehicles were destroyed in the blast.
The attack took place at 9am (0600 GMT) at the western Harithiya gate when many Iraqis were going to work in the zone. It shook buildings across Baghdad.
Staff at the city's Yarmuk hospital, where civilian casualties are generally taken, said they had received seven bodies and were treating 17 people for injuries.
A US military spokeswoman said no one from the American-led forces was wounded or killed in the attack.
At least seven people died
in the car bomb attack
"There were no multinational personnel wounded or killed," she said. "There were Iraqis, but we are waiting for the exact toll. There were several civilian cars destroyed."
Later, two mortar rounds landed in the Green Zone. There were no immediate reports of casualties from these attacks which came a year to the day after toppled Iraqi leader Saddam Hussein was captured by US troops.
A message, purported to be from Abu Musab al-Zarqawi's group, claimed on the Ansar al-Jihad website that they carried out the attack.
"On this blessed day, one of the lions of the martyrdom-seeking brigade struck a gathering of apostates and Americans in the Green Zone," said the statement.
The statement's authenticity could not be confirmed but messages attributed to the group have often appeared on the same website.
The statement was signed by al-Qaida Group of Jihad in the Country of the Two Rivers, the name of al-Zarqawi's organisation, which has purportedly taken credit for some of the deadliest attacks in Iraq.
British consulate attacked
Meanwhile, in the southern city of Basra, mortars have been fired at the British consulate, but details on damage were not immediately clear, a British embassy spokesperson said on Monday.
The attack happened late on Sunday in Basra, 550km southeast of Baghdad, Victoria Whitford said.
British troops patrol Basra
Also on Monday, armed men shot an Iraqi translator working for US forces in the northern city of Kirkuk, severely wounding him and also killing a passerby, police said.
The attack happened at about 8am (0500 GMT) in Kirkuk, 290km north of Baghdad, according to Colonel Anwar Hasan.
Translators and Iraqis working in other support occupations for the American army have been routinely targeted by those who view them as collaborators with the US-led forces.