The announcement came after a six-year government study into the traditional monarchies, some of which were used by the white-minority apartheid rulers as what Zuma described as a divide and rule strategy to weaken black leaders.
Seven of the 13 kingships were approved. The other six will end when the incumbent ruler dies, Zuma told reporters.
"The apartheid regime created its own traditional leadership at the expense of authentic leadership in some communities," Zuma said.
"It was how those in charge divided and disunited people," he said. "We urge all communities to accept the findings in the spirit of correcting the wrongs of the past, and as part of the country's nation-building efforts."
Traditional leaders have little real political power, but can act as arbitrators in local disputes and remain important cultural figures.
Parliament includes a National House of Traditional Leaders, but its role is mainly to advise government on matters where customary law still holds sway - normally family issues like marriage and ritual circumcision.
The decision left in place the Xhosa King Zwelonke Sigcawu and Zulu King Goodwill Zwelithini, representing South Africa's two biggest ethnic groups.
Successors to the six kingships slated for removal will be recognised as lower-ranking traditional leaders.
The apartheid government had created black homelands for each ethnic group and installed their leaders, but no other country ever recognised their independence.
The regions were dismantled after the fall of apartheid.
Zuma stressed that the six were not accused of being apartheid collaborators, but said the decision was meant to defuse historical tensions among rival leaders.
"The finding must help all affected communities to begin the path of acceptance, healing and reconciliation," Zuma said.
"We have always been able to find ways of resolving issues, and of accepting even the most difficult of solutions for the good of the country," he said. "We must face the truth, even if it is uncomfortable, and move forward." The decision is also a cost-cutting measure for the national treasury, which provides each king with an annual subsidy.
Under the shake-up, no traditional kingdoms will be left in the central province of Free State when the kings of the Batlokwa ba Mota and the Bakwena ba Mopeli die.
In the Eastern Cape, the AmaRharhabe and the Amampondo ase-Nyandeni will lose their king. The AbaThembu base-Rhode's king has already died and will not be replaced.
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