The French centre-back has started in six of Arsenal's seven Premier League outings this term, but Wenger said Koscielny needed to rest his problematic tendon for Saturday's clash at Emirates Stadium.
"He will not be available tomorrow," Wenger said of his countryman.
"He has an Achilles problem, which has got worse. He finds it difficult to play with it at the moment.
"You can only trust what the players say. He does not feel ready to play and will not play on Saturday.
"[For] an inflammation of an Achilles tendon, if you wait for it to be better, it can be a short time.
"If you want to get rid of it completely, it is long term."
Meanwhile, Wenger hit out at England manager Roy Hodgson for his usage of midfielder Jack Wilshere.
The Arsenal boss inferred Hodgson was misusing the 22-year-old, who earned full caps in wins over San Marino and Estonia across the international break.
Like Koscielny, Wilshere has been troubled by ankle/foot problems, but Wenger claimed Hodgson deployed him too defensively in England's recent Euro 2016 qualifiers.
"He is back physically to where he was before," said Wenger.
"He is not a ball-winner. I believe he is more a guy who you want to get close to the final third. To keep him deep, you take a big part of his efficiency away.
"He is a guy who likes to penetrate when there are many people. He can provoke free-kicks, he can create openings.
"It would be detrimental to his strengths and a position that is not his strength."
Wenger, though, feels he is one of Hodgson's biggest assets, with the likes of Wilshere, Alex Oxlade-Chamberlain, Danny Welbeck, Calum Chambers and Kieran Gibbs all calling Emirates Stadium home.
And the French tactician believes that Arsenal's fortunes are likely to be paralleled by those of England's accordingly.
"If they can do well at Arsenal, England will be strong," he said.
"That is for sure, because they will play against anybody in the world. The confidence grows."