The Iraqi civilians were just entering the Green Zone at about 8am after making their way through several heavily guarded checkpoints when the three mortars exploded just inside its walls, said police Lieutenant Maitham Abd al-Razzaq.
Iraq's parliament meets in the compound on the banks of the Tigris River, and it also is home to the country's defence ministry and the US and British embassies.
Abd al-Razzaq said it was hard to identify the six fatalities because the powerful explosions and shrapnel from the mortars had severed their limbs and destroyed their identification cards.
But he said one of the wounded Iraqis was a defence ministry employee.
A spokeswoman at the US embassy had no immediate information about the attack, saying officials were still checking to see what had happened.
Other mortar rounds exploded around the same time on the other side of the river near Iraq's interior ministry and the al-Shaab sports stadium, and police were checking to see if any damage or casualties had resulted from the blasts.
The explosions, which were heard across the city, came one day after Iraq's parliament elected a president, two vice-presidents, a parliament speaker and two deputies.
The breakthrough in a long political standoff now gives Jawad al-Maliki, the prime minister designate, 30 days to choose a cabinet from divided Shia, Sunni and Kurdish parties.
Also on Sunday, Iraqi police found the bodies of six young men, bound and with bullet holes in their heads, in Baghdad.
The bodies were found in the city's main Sunni district of al-Adhamiya, where confrontations between its inhabitants and Iraqi forces broke out last week.
Interior ministry sources said the bodies were dumped on the side of a road. Hundreds of bodies, many bearing signs of torture, have been found in Baghdad since sectarian tensions exploded following last February bombing of a shrine the Shia hold as sacred.
The discovery came one day after Iraq's president designated tough-talking Shia politician Jawad al-Maliki to form a national unity government many see as the best way to avert a sectarian civil war.
Al-Maliki, in his first policy speech, said he would work to disband the country's numerous mainly militias, which are suspected to be behind most of the execution-style killings.