The 23-year-old started in a Premier League match against Liverpool, but South Africa have heeded the advice of Burnley manager Vincent Kompany and not chosen the forward.
"Lyle cannot be travelling around the world at this stage and is not in a position to join South Africa for the Cup of Nations," Kompany told South Africa coach Hugo Broos.
Another blow for Bafana Bafana (The Boys) ahead of Group E matches against Mali, Namibia and Tunisia in the Ivory Coast is the absence of injured Strasbourg forward Lebo Mothiba.
The physically imposing 27-year-old hurt his knee in a recent French Ligue 1 match and will be sidelined for several months. Foster and Mothiba are the only South Africans playing for clubs in the top five European leagues.