The legalisation of polyandry was put forward in a green paper published by the Department of Home Affairs.
The plans, part of wider moves by the government to reform the Marriage Act, have upset conservatives and some religious groups.
Polygamy - a man having more than one wife - is already permitted in South Africa.
But Kenneth Meshoe, who is the leader of the opposition African Christian Democratic Party (ACDP), claimed it would “destroy society” if the same marriage rights were extended to women.
Some celebrities have also spoken out over the proposed change.
Reality star Musa Mseleku, who has four wives and features in a programme about his polygamous family, told the BBC: “This will destroy African culture. What about the children of those people? How will they know their identity?”
“The woman cannot now take the role of the man. It’s unheard of. Will the woman now pay lobola [bride price] for the man. Will the man be expected to take her surname?”
Professor Collis Machoko, an academic who has studied the subject, told the BBC that objections to the proposals are about “control”.
He added: “African societies are not ready for true equality. We don’t know what to do with women we cannot control.”
Home affairs minister Aaron Motsoaledi said the debate had descended into a “war of words”.
He added the green paper was not the official policy position of the government and encouraged people to engage in debate on the topics raised.
“It only articulates possible policy options or proposals that are based on inputs received from stakeholders during ministerial dialogues. These proposals will be subjected to public scrutiny,” he added.
South Africans have until the end of June to comment on the proposals.
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