Witnesses said at least two projectiles hit the chicken market in the Ourfalli neighbourhood of al-Sadr City on Saturday.
Abd Al-Jabbar al-Zubaidi, director of a nearby hospital, said several of the wounded were in a critical condition.
It was not immediately clear who had fired the weapons.
Later on Saturday, a roadside bomb killed 14 Iraqis travelling by bus to Baghdad and 12 others were wounded, according to a doctor.
Abbas Wissan al-Shamari, a doctor at the hospital in the town of Iskandariya, 50km south of Baghdad, said the bus was taking people to the capital but he had no immediate further details.
Witnesses said the bus was driving just ahead of a convoy of six US military vehicles when the roadside bomb, a favourite weapon against the occupying forces, exploded.
Local people rushed to the scene from a nearby village to help the injured and dead to hospital, the witnesses said.
They said US troops sealed off the area.
Occupation troops' fire
Also on Saturday, one Iraqi died and three others, all sisters, were badly burned after US troops opened fire in the area, sparking a fire which gutted several cars and spread to homes nearby, residents and doctors said on Saturday.
The US military said it had no information about the incident in al-Sadr City, a poor Shia district where resistance to the US-led occupation is strong.
Residents said US soldiers driving through the district during the night had fired randomly leaving many buildings damaged.
Several buildings had bullet holes in their walls, both inside and outside. Angry residents pointed to the remains of a burnt out minibus and two charred cars. The fire spread to at least two houses.
Five US soldiers were killed and
six wounded on Saturday
"Yesterday, our hospital received one patient who was injured and one who was killed, and three girls from one family who were burnt," Qasim Saddam, a doctor at al-Thawra General Hospital said.
"The girls are between 10 and 14."
In the hospital, one of the girls lay unconscious, the skin burnt off her face and arms. Her younger sister screamed as doctors applied cream to her burns.
Al-Sadr City is the Baghdad powerbase of Shia leader Muqtada al-Sadr and named after his father.
US forces have often been ambushed in the area and there have been heavy clashes there between American soldiers and militiamen.
US marines killed around 30 Iraqi fighters overnight in a firefight near the flashpoint town of Falluja, Colonel John Coleman said on Saturday.
Marines spotted a small group of armed men, one with a mortar, and shot at them near a small village on the banks of the Euphrates, he said at the US base of Camp Falluja, just outside the town.
More than 600 people have been
killed in the Falluja siege
The fighters were joined by about 30 others and the marines called in air support, Coleman, the chief of staff of the Marine Expeditionary Force, told reporters.
He said all the fighters were killed in the action, but gave no other details.
Local doctors say about 600 people were killed earlier this month in an occupation siege of Falluja following the killing of four American contractors.
Bodybags continued to pile up for the US occupation forces. Five US soldiers were killed and six wounded on Saturday when rebels fired two rockets from a truck into their base north of Baghdad, a US military spokesman said.
The spokesman said the attack with two 57mm rockets at the base near the town of Taji started at 5am (01:00 GMT). Three of the wounded were listed as critical with the remaining three in serious condition, he said.
Many vehicles were burnt out in
the market attack
US helicopter gunships were called into action and destroyed the truck from which the rockets were launched. The spokesman did not mention any other casualties.
Two more US soldiers were killed and one wounded on Saturday in an attack on a convoy near the southern Iraqi city of Kut, the local police chief said.
More than 510 US soldiers have been killed in action since US-led forces invaded Iraq and toppled Saddam Hussein.
Saddam's hometown of Tikrit has
been relatively quiet recently
More than 100 of those died this month, making April the deadliest month for US forces in Iraq.
Earlier in the day five rebels who were preparing an ambush near Iraq's holy Shia city of Karbala were killed by a Polish patrol, a spokesman for the Polish contingent said.
Elsewhere in central Iraq, an Iraqi civilian was burnt alive in his vehicle after it came under fire near an occupation troop base early on Saturday, according to hospital sources.
Falah Hasan Abid, 27, was found in his burning Datsun pickup truck near the base located between Kufa and Najaf.
Also on Saturday, a car bomb exploded in Saddam Hussein's hometown of Tikrit north of Baghdad causing several casualties.
"A vehicle-borne improvised explosive device (car bomb) blew up near a shopping centre at about 08:40 this morning (04:40 GMT)," Master Sergeant Robert Powell told Reuters news agency.
"There appear to be a few casualties but we don't have a definite number on civilian casualties."
He said no US soldiers were injured in the explosion. Tikrit,
175km north of the capital has been relatively quiet in recent months despite strong support there for the deposed Iraqi president.