Kolo Toure suffering from malaria
The Liverpool centre-back, 33, fell ill while in Abidjan and before he joined up with the FIFA World Cup-bound squad in Dallas, United States.
Toure is still expected to be available to face Colombia, Japan and Greece in Group C at Brazil 2014.
Ivory Coast team doctor Cyrille Dah said Toure, who has won 107 international caps, was being rested.
"Since Wednesday Kolo has been having treatment and this treatment will end on Friday. We have therefore told him to rest," Dah said.
"He will not participate in the match against Bosnia-Herzegovina, but will return early next week."
Kolo's brother and Manchester City star Yaya is still sidelined with an unspecified muscle injury, while Hannover's Didier Ya Konan is also injured.