The Ivorian Football Federation (FIF) confirmed that the 24-year-old will miss the global showpiece after failing to recover from a thigh injury sustained earlier this month, Africanfootball.com reported.
Akpa had earned a place in Emerse Fae's 26-man squad following an impressive breakthrough with the national team, making five appearances for the Elephants over the past 14 months.
However, the Auxerre defender suffered an adductor muscle injury in training and was subsequently unavailable for his club's final Ligue 1 match of the season against Lille on May 17.
Following further medical assessments, FIF announced that Akpa will not be fit in time for the tournament, which will be hosted by Canada, Mexico and the United States.
His withdrawal represents a significant blow for Fae, who had identified the defender as part of his plans for Ivory Coast's World Cup campaign.
To fill the vacancy, the federation has called up Christopher Operi as Akpa's replacement.
The 29-year-old defender, who primarily operates at left-back, will now have the opportunity to feature on football's biggest stage despite enduring fitness concerns of his own during the latter stages of the season.
Operi missed three of Basaksehir's final five Turkish Super Lig fixtures due to injury and was only fit enough to make the bench in matches against Samsunspor and Gaziantep earlier this month.
Nevertheless, the experienced defender has done enough to convince Fae and his technical team that he can contribute to the Elephants' World Cup challenge.
Ivory Coast will be hoping Operi can quickly regain full fitness as they prepare for the tournament, with the African champions aiming to make a strong impression on the world stage despite the loss of one of their emerging defensive talents.