The Arsenal striker limped out of the 2-2 draw with Everton after scoring the equalizer and could miss the crucial meeting with Besiktas on Wednesday.
The former Montpellier striker replaced Alexis Sanchez at halftime at Goodison Park and rescued a point with an equalizer one minute from time after Everton had initially raced into a two-goal lead.
But the 27-year-old limped off before the whistle blew and Wenger is now concerned that the forward could be an injury doubt for the Gunners's Champions League playoff meeting with Besiktas on Wednesday.
"It is a big game on Wednesday, we hope we can recover," he told Sky Sports. "I hope we have not lost Giroud in the final minute. It's a stretched ankle. It doesn’t look good."
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On the impact the Frenchman made after replacing Sanchez, Wenger added: "I thought we would dominate the game and that we needed some physical presence and I think he had a very good second half. It's great for our belief to know that away from home 2-0 down that with players like that we can come back.
"We always had a good mentality. The competition in England is tough for everybody and the group is still young and improving I think we are really ambitious and we showed that again."
Arsenal faces the Turkish side knowing a win will be enough to take it through to the group stage of the Champions League, following a 0-0 draw in the first leg in Istanbul.