The city's Green Zone, which houses diplomatic missions and much of Iraq's government, also came under renewed attack by rockets or mortars early Wednesday. The U.S. embassy confirmed the shelling, but said there were no immediate reports of casualties.
The bloodshed served as stark reminders of Iraq's continuing instability five years after U.S. troops swept into Baghdad and toppled Saddam Hussein's regime on April 9, 2003. The euphoria of victory soon dissipated - pummeled first by a Sunni insurgency, then Sunni-Shiite slaughter and now battles against Shiite militiamen.
Police said the seven victims in Sadr City - including three children - died when projectiles slammed into a house in the sprawling slum, a stronghold of the Mahdi Army militia of anti-American cleric Muqtada al-Sadr.
Twenty-seven other people were wounded, said a hospital official who asked not to be identified because he was not authorized to speak to the media.
Eyewitnesses in the area said the attack was carried out by U.S. helicopters, but police said the blasts were caused by mortar rounds. The U.S. military had no immediate comment.
As tension rose in Baghdad on the eve of Wednesday's anniversary, the Iraqi military ordered vehicles and motorcycles off the streets from 5 a.m. Wednesday until midnight - a move apparently aimed at preventing Shiite gunmen from moving freely about the city.
The vehicle ban was imposed despite a decision by al-Sadr to call off his "million-strong" demonstration, set for Wednesday, to demand an end to the American military presence.
Still, residents described the situation in much of Sadr City as calmer than the previous days, despite the sounds of explosions and sporadic gunfire.
On Tuesday, Iraqi military spokesman Brig. Gen. Qassim al-Moussawi said a total of 82 militants, 36 civilians and 37 soldiers had been killed since March 16 in fighting in Baghdad, mostly in Sadr City.
The military said Wednesday that an American soldier had died from non-combat related injuries. The name of the deceased was withheld pending notification of the next of kin.
At least 12 American service members have died in Iraq since Sunday, and the shelling of the Green Zone has become almost a daily occurrence.
In Washington, U.S. commander Gen. David Petraeus called Tuesday for anthis summer because of concern over the renewed fighting.
As the number of U.S. forces in Iraq has gradually come down in the past three months, the number of high-profile car bomb and suicide attacks, weekly security incidents, civilian casualties and episodes of ethno-sectarian violence has gone up.
In his testimony to a congressional committee, Petraeus refused to give any indication that more troops could leave Iraq this year, after the last of five brigades ordered into the country for the buildup last year have come home.
U.S. military officials say Petraeus is unlikely to recommend any further cuts until after provincial elections are held in October and that troop strength will not go below 130,000 by the end of the year - about where it was before the surge started, reported CBS News national security correspondent David Martin.