During a two-mile march to the parliament building, the demonstrators were heckled by an angry crowd of men, The New York Times reported. One group of women, encountering men yelling at them and calling them "whores," quickly climbed back on their bus.
Police kept the hecklers away from the marchers.
The law applies only to Shiite Muslims, a minority in Afghanistan. It was passed by parliament and signed by President Hamid Karzai, effectively giving Shiite clerics legal authority to enforce religious beliefs.
The most controversial provisions are those that allow husbands sex on demand, that require women to get permission from their husbands to work or attend school and that turn women into lawbreakers if they do not dress attractively for their husbands.
"Whenever a man wants sex, we cannot refuse," Fatima Hussein, a 26-year-old protester, told the Times. "It means a woman is a kind of property, to be used by the man in any way that he wants."
While the Taliban enforced similar laws when it was in power, the group is Sunni and persecuted the Shiites.
Texas principal bans speaking Spanish, stirs controversy
Caroline Berg Eriksen: Soccer player's wife triggers debate with post-birth selfie