The law, signed by Karzai last month, seeks to regulate family life inside Afghanistan's Shia minority, which makes up about 15 per cent of the population.
It was drafted upon their request because of differences with Sunni Muslims about Sharia, or Islamic, law, the AFP news agency reported.
'Ban on education'
The United Nations Development Fund for Women has said it "legalises the rape of a wife by her husband".
Navi Pillay, the United Nations human rights chief in Afghanistan, has called on the Afghan government to revoke the legislation, saying it is "reminiscent of the decrees made by the Taliban regime".
Under the new measure, Shia women would be banned from working or receiving an education without their husbands' permission, the UN agency said.
They would also be forbidden from leaving their homes except for "legitimate purposes," the agency said.
Asked about the law at a news conference following the Nato summit on Saturday, Obama said the law was "abhorrent" and the US was communicating its views to the Afghan government.
"We think that it is very important for us to be sensitive to local culture, but we also think that there are certain basic principles that all nations should uphold, and respect for women and respect for their freedom and integrity is an important principle."
Gordon Brown, the British prime minister, said he had phoned Karzai to express his "grave concern".
The law "risks putting Afghanistan back to its past, rather than towards it democratic future, where men and women are treated equally," Brown said.
In Kabul earlier on Saturday, Karzai said he had studied the law and did not see any problems with it.
He said Western media outlets had mistranslated the legislation, but he said the law should be reviewed in consultation with scholars and religious leaders.
Sonali Kolhatkar, co-director of Afghan Women’s Mission said: "I doubt this law has been misunderstood. One of the representatives of Afghanistan’s own independent human rights commission saw the full law and saw the president’s signature on it.
"I think he [Karzai] is backtracking. I don’t think he expected the West to react so harshly because women have been suffering innumerable disservices and horrible crimes over the last eight years.
"My guess is that he's panicking. He is trying to please the warlords who dominant the parliament that is his power base. He is completely unpopular with his own population for not standing up to the US and Nato."
Fawzia Kofi, a member of the Afghan parliament, said that the law undermines all advances for Afghan women in the last seven years.
She told Al Jazeera that the main victims are women and children.
Critics have accused Karzai of signing the law to court Shia votes in the country's August presidential election.