Debuchy was stretchered off with 10 minutes to go at Emirates Stadium and the France international full-back looked in some pain.
Wenger has conceded Debuchy's problem 'doesn't look good' and he is waiting to learn the full extent of the summer signing's injury.
"Debuchy has a badly sprained ankle," said Wenger. "How long will he be out? I don't know, but it doesn't look good.
"People told me they need a bit more time to assess how long he will be out but it's a bad ankle sprain."
Deadline day signing Welbeck, meanwhile, was brought off in the closing stages after earlier missing a golden 12th minute chance to put Arsenal in front.
Wenger added of Welbeck: "He had cramps and he should be okay.
"He did well. I believe that he needs to develop his link play with our players but that is a bit normal.
"It's sad that he couldn't take his chance but overall every time he had an opportunity to find some space he looked dangerous.
"There are some things to work on with him to integrate him well into our game but I'm happy with his first game."
Sergio Aguero had given City a first-half lead before goals from Jack Wilshere and Alexis Sanchez turned the game in Arsenal's behavior only for Martin Demichelis to head an 83rd-minute equalizer for the Premier League champions.
City boss Manuel Pellegrini was unhappy with referee Mark Clattenburg after the game and Wenger also had some concerns.
"Both managers were frustrated because I heard Pellegrini was not happy with some of the decisions of the referee," said Wenger. "All of them? Yes, maybe.
"In the first half they stopped us from going out on the break by systematically fouling. Even if the referee gave the foul, the yellow card came a bit too late in my opinion to be completely satisfied and get rid of that systematic foul that stopped us in our game.
"We had great pace in our game today and they stopped that in an intelligent way. They are a mature team and intelligent but it was not an easy game to referee as well."
When asked if there were fouls in the build-up to Arsenal's goals, Wenger replied: "I heard that. There were situations where it was a real fight for the ball and we may have fouled, they may have fouled. We made one and they made one again, and the guy came out with the ball. The referee decided to let it go and he let it go.
"I don't think it was a vicious game but it was just a committed one. When the players went for the ball, they went in with commitment.
"I don't know, we'll have to watch it again. I don't think that explains why we scored after because there was a lot to do after that."