Edwin Samotse is accused of murder in his home country, spokesman Mayihlome Tshwete said in a statement.
Two home affairs officials have been suspended for allegedly arranging his transfer back to Botswana on August 13 without authority to do so.
Samotse was in custody at the Polokwane police station while the Botswana government sought his extradition.
The South African government asked for an assurance that Samotse would not face the death penalty if he were extradited. The Botswana government did not agree to this.
In two previous cases, the courts decided that the South African government and its officials could not deport people to countries where capital punishment was used, if such an assurance was not given.
On August 13 the High Court in Pretoria issued a similar order in the Samotse matter, Tshwete said.
“Officials from the department of home affairs, without prior knowledge of the director general and without any authority, secured the release of Mr Samotse from the Polokwane police station and transported him to the Groblersbrug port of entry between South Africa and Botswana, where they handed him over to Botswana officials.
“Accordingly, the department condemns these actions as unlawful and unconstitutional.”
Tshwete said the department was trying to resolve the matter with the Botswana government.
Lawyers for Human Rights said in a statement on its website that it and Legal Aid SA would approach the High Court in Pretoria on Monday. They wanted the court to compel home affairs to find Samotse and get an assurance from the Botswana government that he would not face the death penalty if convicted.