The draft law would limit Cambodians to having only one husband or wife. Parliament began debating the law on Tuesday.
"This law is aimed at protecting dignity, strengthening harmony within the family and mutual respect between a husband and a wife," reads the law, which was introduced by 63 lawmakers, many of them women.
The proposed law would outlaw polygamy and incest, making extra-marital relations punishable by between a month and a year in prison, plus a fine of up to $250.
Members of parliament from the ruling Cambodian Peoples party said the law would help to strengthen social morality in the impoverished nation.
Ek Sam Ol, a member of parliament from the ruling party, said:"This law is a tool to ensure that Cambodian families ... are dignified and prosperous in the future."
Opposition MPs say the law would mark a throwback to the Khmer Rouge government that ruled the country from 1975-79, when extra-marital affairs were punished by execution.
Eng Chhay Eang, of the opposition Sam Rainsy party, said: "The parliament should not pass this law because it does not benefit the nation or the development of the country."
Hun Sen, the prime minister, proposed the law five months ago, after he publicly grumbled about government officials bringing their mistresses instead of their wives to official functions.
Although polygamy is a common practice in traditional Khmer families, the law would most obviously affect Prince Norodom Ranariddh, the leader of the royalist Funcinpec party, who is often seen with his mistress.