Photo: AFP/GETTY
The law, which has not been publicly released, is believed to state women can only seek work, education or doctor's appointments with their husband's permission.
Only fathers and grandfathers are granted custody of children under the law, according to the United Nations Development Fund for Women.
Opponents of the legislation governing the personal lives of Afghanistan's Shia minority have said it is "worse than during the Taliban".
Mr Karzai has been accused of electioneering at the expense of women's rights by signing the law to appeal to crucial Shia swing voters in this year's presidential poll.
While the Afghan constitution guarantees equal rights for women, it also allows the Shia community, thought to represent 10 per cent of the population, the right to settle family law cases according to Shia law.
The Shiite Personal Status Law contains provisions on marriage, divorce, inheritance, rights of movement and bankruptcy.
The bill passed both houses of the Afghan parliament, but was so contentious that the United Nations and women's rights campaigners have so far been unable to see a copy of the approved bill.
Shinkai Zahine Karokhail, a female MP, said the law had been rushed through with little debate.
She told the Guardian newspaper: "They wanted to pass it almost like a secret negotiation, "There were lots of things that we wanted to change, but they didn't want to discuss it because Karzai wants to please the Shia before the election."
The Afghan justice ministry confirmed the law had been signed, but said it would not be published until technical difficulties had been overcome.
A spokesman for President Hamid Karzai would not comment.
An act signed into law by Afghan President Hamid Karzai last month dramatically rolled back the rights of women in that country, according to human rights groups and a United Nations report on the bill by the United Nations Development Fund for Women.

The Afghan government has not provided a copy of the text of the Shia Family Law to the UN or to other outside groups requesting it, citing "technical problems", however, the UN and opposition politicians say that the bill contains numerous provisions restricting the rights of women, such as giving their husbands priority in court; requiring the husband's permission to leave the house, obtain education or employment, or to see a doctor; and reserving the custody of children to male relatives.

In its most controversial provision, though, the law's Article 132 requires wives to submit to their husbands' sexual demands, and says that a husband can expect sex with his wife once in every four days except in the event of illness. The United Nations argues that this is equivalent to spousal rape. Spousal rape is specifically prohibited in 45 countries worldwide and may be prosecutable by existing rape statutes in others.

The circumstances of the bill's passage have raised questions as well, with Senator Humeira Namati saying that the bill was not read out or debated in the House of Elders, the Afghan National Assembly's upper house and Shinkai Zahine Karokhail of the House of the People stating the bill received only limited debate in the lower chamber. "They wanted to pass it almost like a secret negotiation," Karokhail told the ''Guardian''. "There were lots of things that we wanted to change, but they didn't want to discuss it because Karzai wants to please the Shia before the election." Namati calls the new law "worse than the Taliban".

burqas cross a market in Parwan Province, Afghanistan.According to Karokhail and others, the law received Karzai's support in order to boost his popularity among Afghanistan's Shi'a population, which comprises an estimated ten per cent of the country, ahead of an upcoming election in August. A Monday ruling by the Afghan Supreme Court has allowed Karzai to remain in power in the interval between the expiration of his term on May 21 and the upcoming Afghan presidential election in August. It is unclear whether the law would apply only to Shi'a persons or to all Afghans.

Nonetheless some changes were made to the bill; the proposed minimum age of marriage for girls was raised to 16 from aged 9 and temporary marriage is not provided for. MP Shukria Barakzai says that "before this was passed family issues were decided by customary law" and that the new law, while not perfect, is an "improvement". MP Ustad Mohammad Akbari defended the bill as well, saying it protects women's rights: "Men are stronger and women are a little bit weaker; even in the west you do not see women working as firefighters."

A spokesman for Mr. Karzai gave reporters no comment.