The defender was stretchered off in Arsenal's UEFA Europa League semi-final second-leg clash with Atletico Madrid earlier this month and after having an operation he may not feature again until the end of the year.
"Koscielny is devastated," Wenger said, per the Mirror's James Whaling. "He has had surgery and is out for six months. You will not see him until December at best. He will miss the World Cup. You always try to be positive. Try and support people when they suffer."
According to Goal's Chris Wheatley, he added: "What is unusual, in his case he had a [Achilles] tendinopathy for a long time and usually they do not rupture. In this case it went, and I don't know why."
James Olley of the Evening Standard had anticipated it would be a serious injury at the time:
James Olley @JamesOlley
Koscielny looks in a huge amount of pain here. Hard to tell from where I'm sat but if that is his Achilles, it could be serious. He's already managing an Achilles problem on a daily basis. He was beating the ground in pain just now. Lengthy stoppage already. Chambers coming on.
The Frenchman is now past his prime, but he has been Arsenal's best defender for much of the last decade, and his loss is a blow to the club and the French national side ahead of the World Cup.
He will be 33 before he returns to action for the Gunners, for whom a new centre-back will become an even bigger priority this summer.
A new central defender was already much-needed after a campaign in which Arsenal have shipped 48 goals in 36 Premier League games, but they may even need two additions there now with Koscielny set to miss at least half of next season.
It will provide an added challenge for Wenger's successor, who will already have their hands full with reversing years of decline under the coach.