The law has been described as "oppressive" for women
Nato's head says it could be difficult to persuade European countries to contribute more troops to Afghanistan because of controversial new laws.
Jaap de Hoop Scheffer said the planned laws violated human rights and were unjustifiable when Nato troops were dying to protect universal values.
Critics say the law limits the rights of women from the Shia minority and authorises rape within marriage.
Aides to President Karzai insist the law provides more protection for women.
Nato Secretary General Jaap de Hoop Scheffer told the BBC's Mark Mardell: "We are there to defend universal values and when I see, at the moment, a law threatening to come into effect which fundamentally violates women's rights and human rights, that worries me."
Nato chief's Afghan law fears
He added: "I have a problem to explain and President Karzai knows this, because I discussed it with him. I have a problem to explain to a critical public audience in Europe, be it the UK or elsewhere, why I'm sending the guys to the Hindu Kush."
France's Human Rights Minister Rama Yade also expressed her "sharp concern" at the law, saying it "recalls the darkest hours of Afghanistan's history".
The UN earlier said it was seriously concerned about the potential impact of the law.
Human rights activists say it reverses many of the freedoms won by Afghan women in the seven years since the Taleban were driven from power.
They say it removes the right of women to refuse their husbands sex, unless they are ill.
Women will also need to get permission from their husbands if they want to leave their homes, unless there is an emergency.
The law covers members of Afghanistan's Shia minority, who make up 10% of the population.
It was rushed through parliament in February and was backed by influential Shia clerics and Shia political parties.
Defenders of the law say it is an improvement on the customary laws which normally decide family matters.
A separate family law for the Sunni majority is now also being drawn up.
Nato is holding its annual summit in Strasbourg.
President Obama is to present his new Afghan strategy to his allies.
Ahead of the meeting, a number of leading charities warned that an increase in military deployments in Afghanistan could lead to a rise in civilian casualties.
They called on Nato leaders gathering in Strasbourg to do more to protect the population.
Last year more than 2,000 civilians were killed in Afghanistan.
In a report titled Caught in the Conflict, 11 aid groups including Oxfam, ActionAid and Care called on Nato to change the way it operates.
"The troop surge will fail to achieve greater overall security and stability unless the military prioritise the protection of Afghan civilians," Matt Waldman, head of policy for Oxfam International on Afghanistan, said.
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