His place is to be taken by left-back Christopher Operi, who was in the squad for the Africa Cup of Nations finals in Morocco at the turn of the year but then was injured when the Ivorians beat South Korea and Scotland in friendly internationals in March.
Akpa, who has been capped five times, suffered an adductor injury at training with his French club AJ Auxerre and missed the last weekend of Ligue 1 action earlier this month.
Operi, who plays at Turkish club Istanbul Basaksehir, has joined the Ivorian squad at the training camp in Paris.
Ivory Coast have a friendly match against France on June 4th in Nantes before heading to the World Cup where they take on Ecuador, Germany and Curacao in Group E.