The Ivorian should be able to return to training ahead of the tournament in Brazil after falling ill on a trip to Abdijan before he arrived in Dallas for a training camp
The 33-year-old, who previously suffered with the illness in 2008, fell ill during a trip to Abdijan prior to joining up with the Elephants' World Cup squad in Dallas and will now sit out Saturday's match in St. Louis.
Toure's condition is not thought to be serious and team doctor Cyrille Dah believes he will return prior to his side's World Cup opener against Japan in Recife on June 15.
"Since Wednesday Kolo has been having treatment. This treatment will end on Friday," he told the Ivorian Football Federation's official website.
"We have therefore told him to rest. He will not participate in the match against Bosnia-Herzegovina, but will return early next week."
Toure has made 107 appearances for his country, scoring six goals, and appeared 20 times in the Premier League during his debut season at Anfield.