The centre-half is currently sidelined with a calf problem and sat out Saturday’s 2-2 north London derby draw at Tottenham due to the injury.
Wenger revealed on Monday morning that Koscielny is likely to miss this weekend’s game as well.
Speaking at a news conference at Arsenal’s London Colney training ground on Monday morning, Wenger said: “Laurent will be short for Hull. he has a chance to be available for the weekend, but I think even for then he will be short.”
The Arsenal boss went on to confirm that goalkeeper Petr Cech is set to be sidelined for around four weeks due to his own calf problem.
He continued: “Petr’s scans were better than expected, but it will still be four weeks for him. So after the international break.”
Arsenal will be without the suspended Francis Coquelin after his sending off during the north London derby at White Hart Lane.
Wenger added: “We lose Coquelin from his bad tackle on Saturday and everyone else looks available.
“I have to see how everybody has recovered today but overall we should have the same squad that went to Tottenham plus Alex Iwobi will certainly be added to the squad. ”
Arsenal take on Hull looking to book their place in the quarter-finals of the FA Cup, where they would face Watford at home.
MORE: The latest football news