The proposed law would also make it illegal for a Shia woman to leave her house without her husband's permission.
The proposed Shia family law has cast a shadow over an international conference in Europe on Afghanistan's future.
According to the Globe and Mail, Canadian Defence Minister Peter MacKay said he would use this week's NATO summit to put 'direct' pressure on his Afghan counterpart to abandon the legislation.
"That's unacceptable - period. We're fighting for values that include equality and women's rights. This sort of legislation won't fly," the paper quoted him, as saying.
Critics say Afghan President Hamid Karzai approved the law in advance of his country's elections in the hope of winning critical swing votes from conservative Shia men.
Canadian officials have contacted Karzai's office and also raised their concerns with senior Afghan cabinet ministers. They say it's not yet clear what's in the law, but they're trying to find out.
U S Secretary of State Hillary Clinton reportedly upbraided Karzai over the proposed law during this week's 80-country Afghanistan summit in The Hague.
Several Conservative cabinet ministers have denounced the measures, as have spokesmen for Prime Minister Stephen Harper.
Liberal Leader Michael Ignatieff said he's outraged by the legislation and Canada must make it clear to Karzai that it's unacceptable.
International Co-operation Minister Bev Oda said she was in 'disbelief' when she first heard about the legislation. She noted that the equality of the sexes is a key Canadian objective in Afghanistan.
"We've invested a lot, we've put a lot of energy and resources into that," Oda said.
"It's very problematic. It's of great concern, and it is going to be a difficulty for Canada - because of our investment and our commitment to human rights, the rule of law, and equality. . . the steps we're taking, the investment we're making, and the work we're doing," she concluded.