The 1996 African champions finished third in Group C behind Ghana and Sudan who beat them 2-0 on Sunday in Khartoum to snatch the runner-up spot.
Safa announced the departure on social media following a review of the team's qualifying campaign.
Ntseki came to prominence as coach of the the country's under-17 side.
He was appointed caretaker boss after the departure of Stuart Baxter who led South Africa to the quarter-finals at the Cup of Nations in 2019 in Egypt.
South Africa's new coach will be tasked with steering the team to the 2022 World Cup in Qatar.
They will face familiar foes in the shape of Ghana and Ethiopia. Zimbabwe also feature in their qualifying group.
The 10 pool winners advance to a play-off round in November where the victors will earn a place in Qatar.
