The country’s electoral commission has not given a reason.
However, his 2021 conviction, and jailing, for contempt of court would appear to disqualify him.
Mr Zuma’s backing of the new uMkhonto weSizwe (MK) party has been seen as a possible threat to the governing African National Congress (ANC), which has suspended Mr Zuma.
He served as president from 2009 to 2018.
His was the first name on the MK’s candidate list, but the electoral commission received objections to him potentially becoming a member of the National Assembly.
“In the case of former President Zuma, yes, we did receive an objection, which has been upheld,” said electoral commission head Mosotho Moepya on Thursday, without further explanation.
Mr Zuma received a 15-month prison sentence in 2021 for contempt of court and the constitution says anyone who has had a prison sentence of longer than 12 months is not eligible to run for election.
The IEC said that the ruling did not prevent the MK party from taking part in the 29 May poll, News24 reports.
For the first time since the start of the democratic era in 1994, the ANC’s vote share could fall below 50%, according to several opinion polls. The MK party is seen as popular in Mr Zuma’s home region of KwaZulu-Natal.