King Buyelekhaya Dalindyebo reported to prison after his legal attempts to overturn his conviction failed.
The case against King Dalindyebo as related to a dispute he had with some of his subjects about two decades ago.
He comes from the Thembu clan, to which Mr Mandela, South Africa’s first black president, belonged.
He is the first monarch to be jailed in South Africa since minority rule ended in 1994.
King Dalindyebo, 51, ascended to the throne in 1989, and has about 700,000 subjects.
South Africa has 10 officially recognised monarchs representing different ethnic groups and clans.
They play a largely ceremonial role, and attend to minor disputes within their communities.
King Dalindyebo was accused of kidnapping a woman and her six children, setting their home on fire and beating up four youths, one of whom died, because one of their relatives had failed to present himself before the king’s traditional court.
He handed himself to prison authorities in the eastern city of Mthatha in compliance with a court order after a judge refused to extend his bail on Wednesday, the justice ministry said in a statement.
Earlier, Justice Minister Michael Masutha turned down his request for a retrial, saying there was no legal justification for doing so.
King Dalindyebo had maintained his innocence, saying he disciplined his subjects under customary law.
Sentencing him in October, the Supreme Court of Appeal said: “His behaviour was all the more deplorable because the victims of his reign of terror were the vulnerable rural poor, who were dependent upon him. Our constitution does not countenance such behaviour.
“We are a constitutional democracy in which everyone is accountable and where the most vulnerable are entitled to protection.”
Many people feel King Dalindyebo has disgraced the royal family, and that he will be hard-pressed to find any sympathy, correspondents say.
There is already talk of his son, Prince Azenethi Dalindyebo, being crowned as the next monarch.
King Dalindyebo defected from the governing African National Congress (ANC) to the opposition Democratic Alliance (DA) party during his legal battles.
The DA revoked his membership following the ruling of the Supreme Court of Appeal.