Zuma said that his imprisonment was excessive, unjust and might kill him if he catches COVID-19 in prison, Reuters said.
The constitutional court sentenced Zuma to 15 months in jail on Tuesday for failing to appear at the corruption inquiry led by Deputy Chief Justice Raymond Zondo in February.
He was given five days to appear before police, but it was unclear whether he will go willingly. His supporters have gathered in his home town of Nkandla to resist his arrest.
In an affidavit submitted on Friday, Zuma said going to jail would put him at great risk.
Since being ousted by his successor, Cyril Ramaphosa, in 2018, Zuma has faced several legal manoeuvres aimed at bringing him to justice on allegations of grand corruption during and before his time as president.
These include Zondo's inquiry and a separate court case relating to a $2 billion arms deal in 1999, when Zuma was deputy president.
Zuma also called the sentence a "political statement of exemplary punishment". He has maintained all along that he is the victim of a political witch hunt, and that Zondo is biased against him.
KI/PR