The country's electoral commission, or IEC, has not given a reason.
However, his 2021 conviction and jailing for contempt of court would appear to disqualify him.
His backing of the new uMkhonto we Sizwe (MK) party has been seen as a possible threat to the governing African National Congress (ANC), which has suspended Mr Zuma.
The 81-year-old served as president from 2009 until 2018, when he had to step down because of corruption allegations.
Mr Zuma's new party is named after the ANC's former military wing, and he sees himself as the true heir to the governing party's revolutionary roots.
The ANC had wanted South Africa's electoral body to deregister MK, but that request was rejected on Tuesday.
Mr Zuma has been leading the MK party's campaign and was the first name on their candidate list, but the electoral commission received objections to him potentially becoming a member of the National Assembly.
Rather than voting directly for a president, South Africans elect members of the National Assembly. The head of whichever party can muster a majority is likely to become the country's leader, though it could put forward another candidate.
"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.
"The party that has nominated him has been informed," Mr Moepya told journalists.
Mr Zuma has until 2 April to appeal against the decision.
MK spokesman Nhlamulo Ndlhela told AFP news agency the party was "looking at the merit of that objection but we will of course appeal it".
