However, another academic, Dr. John Akokpari from the University of Cape Town, said South Africa should seriously consider giving Mugabe asylum as the country was Zimbabwe's biggest trading partner in the region.
The 93-year-old had led the African country for 37 years, but resigned as impeachment proceedings began against him. British Prime Minister Theresa May said on Tuesday that Mugabe's resignation gave Zimbabwe the chance to forge a new path, free from oppression.
The ANC has also praised the Zimbabwean military for its "peaceful" handling of the situation to ensure a "smooth transition", in the wake Mugabe's resignation.
Zimbabwe is due to hold national elections no later than September 2018.
Parliament Statement on Latest Developments in Zimbabwe
James Selfe, the chairman of the DA's federal executive, said the party had written to President Jacob Zuma and his foreign minister to warn that taking in Mugabe would be an illegal act in terms of local refugee legislation.
"President Mugabe condoned human rights violations, defended criminal actions of his officials and allowed a culture of impunity for grotesque crimes to thrive". "In recent days, we have seen the desire of the Zimbabwean people for free and fair elections and the opportunity to rebuild the country's economy under a legitimate government".
That decision was seen by many as clearing the way for Mr Mugabe's wife, Grace, to succeed her husband as leader.
Britain wants Zimbabwe to re-join the global community following the resignation of Robert Mugabe, Prime Minister Theresa May said on Wednesday. Reports, however, indicate that army tanks had started withdrawing from their positions following news of Mugabe's resignation.More news: Clippers G Patrick Beverley undergoes knee surgery