The government is a major shareholder in the country's biggest companies which have already been forced to fall in line, but the new law will apply to companies the Government holds no share in, about 500 companies in all.
The law says that companies that miss the quota will be closed down by force.
The Confederation of Norwegian Enterprise criticised the move as unnecessary and said women were taking a bigger role in business without government interference. "This is an unnecessary law for female representation. Business should pick board members on competence and not on statistics," the group's director, Sigrun Vaageng, said.
"This is about getting power and influence. It is a historical moment," Karita Bekkemellem the Minister for Equality said. Ms Bekkemellem reportedly left open the option to pay off the government instead if companies missed the deadlines.