The Confederation of African Football said Jordaan, who led the 2010 World Cup organizing committee, came fourth of five candidates in a poll choosing two delegates to join FIFA's ruling panel.
Algerian federation president Mohamed Raouraoua won the election with 39 votes and Ivory Coast federation president Jacques Anouma was second with 35.
Jordaan received 10 votes from the 53 national members who make up CAF.
Jordaan was seeking to follow playing greats Michel Platini of France and Franz Beckenbauer of Germany, who organized successful World Cups then joined the inner circle of football's world governing body.
Raouraoua will replace disgraced Amos Adamu, who FIFA suspended for seeking bribes during the 2018 and 2022 World Cup bidding contests. Adamu was ineligible.
The Algerian official will formally join FIFA's executive committee on 1 June at its congress in Zurich.
Anouma was re-elected to serve a second four-year term.
Africa sends four delegates to the FIFA ruling panel, but the seats of CAF President Issa Hayatou of Cameroon, and Hany Abo Rida of Egypt come up for election in 2013.
Jordaan gained global recognition for his work helping South Africa overcome doubters that it could stage a successful, safe and profitable World Cup.
However, he did not rise through the committee hierarchy of CAF like Raouraoua and Anouma.
Jordaan polled fewer votes than the 12 given to Suketu Patel of Seychelles, another member of the CAF executive committee. A fifth candidate, Ibrahim Galadima of Nigeria, received five votes.
The election during the CAF annual assembly was observed by FIFA President Sepp Blatter and the two men considered the strongest candidates to succeed him, UEFA President Platini and Mohamed Bin Hammam, the Qatari who leads the Asian Football Confederation.
Blatter is standing for election for a fourth four-year term on 1 June.