Debuchy received oxygen before being stretchered off the field after landing awkwardly on his ankle toward the end of the contest at the Emirates Stadium.
Wenger says that the club's medical staff are yet to determine the severity of the injury, but admits that it "does not look good" for the French right-back.
"Debuchy has a badly sprained ankle. How long will he be out? I don't know, but it doesn't look good," Wenger told the club's official website.
"People told me they need a bit more time to assess how long he will be out but it's a bad ankle sprain."
However, Martin Demichelis was on hand to head home an 83rd-minute equaliser to deny Arsenal their second win of the Premier League season.