This should be irrespective of the position the candidate concerned might hold in his or her political party, he said.
In a statement afterwards, Gibson said Winnie Madikizela-Mandela had chosen, despite the many crimes in which she was alleged to have been involved, not to apply to the Truth and Reconciliation Commission for amnesty.
"In the light of this failure, the Democratic Party cannot understand why she has not been prosecuted for any of these alleged crimes."
If it transpired at the TRC hearings this week that there was a prima-facie case against her on any count, the DP called on the government to prosecute her without delay.
It was important to demonstrate that nobody was above the law.
"We are also extremely concerned that Madikizela-Mandela is being touted as a possible future Deputy President of the ANC and of South Africa.
"Should this ever happen, our country's image will suffer enormous harm and the moral foundations of democracy would be undermined," Gibson said.