The French Football Federation confirmed on Friday evening that the centre-back would not be able to play in Russia.
"It's a very big blow for the France team," coach Didier Deschamps said on http://www.fff.fr.
The defender was carried off on a stretcher early on during the 1-0 defeat at the Wanda Metropolitano.
The 32-year-old lost his footing while moving towards Diego Costa off the ball and was in obvious distress as he clutched his lower leg.
Gunners boss Arsene Wenger revealed after the game that he feared the worst for Koscielny, who has been nursing an Achilles problem for most of the season.
Koscielny, who has 51 caps, had already announced he planned to retire from international football after the World Cup.
Deschamps added: "I am really very sad for Laurent, because this World Cup was also a very important moment for him in his career and I wish him a lot of strength in his comeback, because I'm sure he still has some great things to come."
France will face Australia, Peru and Denmark in Group C at the World Cup, with their first game - against the Socceroos - scheduled for June 16.
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