The bill, which amended existing marriage legislation, was passed yesterday to formalise customary law about marrying more than one person.
The proposed bill had initially given a wife the right to veto the husband's choice, but male members of parliament overcame party divisions to push through a text that dropped this clause.
"When you marry an African woman, she must know the second one is on the way, and a third wife... This is Africa," MP Junet Mohammed told the house, according to Nairobi's Capital FM.
"Any time a man comes home with a woman, that would be assumed to be a second or third wife," said Samuel Chepkong'a, chairman of the Justice and Legal Affairs Committee, the Daily Nation newspaper reported.
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"Under customary law, women or wives you have married do not need to be told when you're coming home with a second or third wife. Any lady you bring home is your wife," he added.
"We know that men are afraid of women's tongues more than anything else," female legislator Soipan Tuya told fellow MPs, according to Capital FM.
"But at the end of the day, if you are the man of the house, and you choose to bring on another party - and they may be two or three - I think it behoves you to be man enough to agree that your wife and family should know," she added.
The bill must now pass before the president to be signed before becoming law.