The Lazio playmaker, who has become an important part of Rabah Saadane's team in recent months, had been told that a knee injury he had been carrying will not heal in time for the tournament, which begins in South Africa on 11 June.
The 26-year-old France-born player is now set to undergo surgery to fix the problem with the news coming after a meeting with the medical team of the Desert Foxes, including doctor Hakim Chalabi, coach Saadane and Mohamed Raouraoua, the president of the Algeria Football Federation (FAF).
Speaking to television station Arryadia immediately after the announcement, Meghni said: "I'm very sad about this. I've been fighting this injury for months but it didn't heal properly. It would have been risky for me to play and things could have gotten even worse. The decision was taken and I need to accept it. The doctors know what they're doing and they gave their final say on the matter."
Meghni said he still felt part of the team and wished the players all the best for the tournament. "The manner in which I was informed about it and the sadness on the face of the FAF president somehow comforts me a bit because it showed me that I'm in a family," he said. "My team-mates also shared my sadness with me. Things didn't work out, I have to accept this. I'm definitely sad but life goes on and I hope that the team makes it to the second round."
The North Africans are in Group C for the finals, alongside England, the United States and Slovenia.