"We will know tonight. He has an exploration of his ankle tonight," Wenger told reporters ahead of Saturday's Premier League match at Aston Villa when asked about the French international.
"They are going to look at how the ligament is damaged and after that we'll know. If he doesn't need surgery it will be six weeks. If he does, it will be three months. At the moment we don't know."
The 29-year-old Debuchy, who joined the Gunners from Newcastle in July, suffered the injury during a 2-2 draw with Manchester City last weekend.
Wenger had better news to report on Calum Chambers, who has recovered from tonsillitis, as well as midfielders Mathieu Flamini and Wilshere.
The manager said all would be available for the game at Villa Park, with concern about Wilshere's ankle receding after he picked up a knock in the 2-0 Champions League group defeat at Borussia Dortmund on Tuesday.
"It was his left ankle and it was only a click that made him turn a little bit his ankle, so he's alright," the Frenchman said of Wilshere.
Arsenal are still without injured winger Theo Walcott, Serge Gnabry and Olivier Giroud while Yaya Sanogo has a hamstring injury.
Left back Nacho Monreal will also miss the Villa game due to a back problem that kept him out of the squad for the Champions League match.
Wenger said Arsenal were eager to bounce back from the Dortmund defeat against unbeaten opponents currently second in the league.
"We want to respond... we came out of Saturday's game thinking we had a very good performance and on Tuesday night we didn't so it's important we come back," he said.
"We have confidence in our strength and we want to show that we can perform in an important game tomorrow."
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
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