Zuma told the inquiry on Monday that he had been the victim of a plot to get rid of him and that he could trace that conspiracy to foreign intelligence services and the apartheid government in the 1990s.
Appearing again on Tuesday, Zuma said his personal assistant received a phone call late on Monday from an unknown caller threatening to kill Zuma and his children.
The country's deputy chief justice, Raymond Zondo, who is overseeing the inquiry, said the threats were unacceptable.
There was no immediate comment from the police.
Zuma, ousted by the governing African National Congress (ANC) in February 2018 and replaced by President Cyril Ramaphosa, has consistently denied wrongdoing over his nine years in power.
His appearance at the inquiry caps a dramatic fall from grace for a politician who long dominated the country`s politics.
The inquiry is investigating allegations that Zuma allowed three Gupta brothers, friends of his, to plunder state resources and influence senior government appointments.
Several former officials have told the inquiry that the Guptas were privy to information about senior government appointments.
On Monday Zuma denied that he had done anything unlawful with the Guptas or that he had discussed anything with them that he should not have.
The Gupta brothers, who denied the allegations at the time, left the country around the time that Zuma was ousted.
Zuma's appearance at the inquiry caps a dramatic fall from grace for a politician who long dominated the country`s politics