The Lazio midfielder was informed on Tuesday that he needs knee surgery and was accordingly dropped from Rabah Saadane's list.
"I'm very sad about this. I've been fighting this injury for months but it didn't heal properly," said Meghni.
"It would have been risky for me to play and things could have gotten even worse."
Saadane in tears
As reported by Al-Jazeera, manager Saadane had to make the difficult decision as he broke down in tears during a press conference in Switzerland.
The veteran coach said he couldn’t comment on the blow in an emotional announcement, thought to have shocked the Algerian community.
In the same manner, Algeria captain Yazid Mansouri reflected the impact of Meghni's absence on the Fennecs.
"Honestly, we are very sorry and depressed that Meghni will have to miss the World Cup," Mansouri was quoted by Elheddaf newspaper.
"It really affected us as a team, but we have to move on and think positive. It was risky for him to play and I am sure he will make a strong comeback."
Algeria meet Ireland in a warm-up in Dublin on Friday, amid a number of injury concerns as well.
Antar Yahia, Madjid Bougherra, Hassan Yebda and Carl Medjani will not be risked against the Irish as Saadane prepares to announce his final squad.