Police have also found 22 bodies across Iraq, 20 of them in Baghdad, of men tortured and shot dead in apparent sectarian attacks.
The latest violence came a day after a suicide bombing in a coffee-shop in the northern town of Tuz Khurmatu killed 28 people.
In the attack on the market in the town of Mahmudiyah, 30 km from Baghdad, two car bombs and four mortars reportedly hit the market before gunmen in six cars randomly opened fire.
Three of the attackers have been arrested.
In the past few weeks, rebels have launched major attacks on markets across Iraq, causing heavy civilian casualties, with many appearing to be sectarian in nature.
Canberra 'to compensate family'
Meanwhile Iraq's trade minister Abdel Falah al-Sudani said wheat trade with Australia will continue after Canberra agreed to compensate the family of one his bodyguards killed by Australian troops last month.
One of Mr Sudany's bodyguards was killed and four people wounded when Australian security forces in Baghdad shot at the bodyguards' car as it approached their convoy on June 21.
An Australian military inquiry later cleared the soldiers of any
wrongdoing, angering the minister, who demanded compensation and for the inquiry be reopened.
In other news, Japanese premier Junichiro Koizumi said his country had completed withdrawing its troops from Iraq, ending their first military mission in a conflict since World War II.