The legislation is referred to as the Ja'afari Law, named after the sixth Shi'ite imam
About two dozen Iraqi women demonstrated on Saturday in Baghdad against a draft law approved by the Iraqi cabinet that would permit the marriage of nine-year-old girls and automatically give child custody to fathers.
"On this day of women, women of Iraq are in mourning," the protesters shouted.
"We believe that this is a crime against humanity," said Hanaa Eduar, a prominent Iraqi human rights activist. "It would deprive a girl of her right to live a normal childhood."
Shi'ite Islamists have come to lead the government and look to impose their religious values on society at large.
It describes girls as reaching puberty at nine, making them fit for marriage, makes the father sole guardian of his children at two and condones a husband's right to insist on sexual intercourse with his wife whenever he wishes.
The legislation is referred to as the Ja'afari Law, named after the sixth Shi'ite imam Ja'afar al-Sadiq, who founded his own school of jurisprudence.
The draft was put forward by Justice Minister Hassan al-Shimari, a member of the Shi'ite Islamist Fadila party.
Mohammed, the Muslim prophet, married a six-year-old, so Islamic law has no problem with raping nine-year-olds.