The former Montpellier striker replaced Alexis Sanchez at half-time at Goodison Park and rescued a point with an equaliser 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 play-off meeting with Besiktas on Wednesday.
He told Sky Sports: "It is a big game on Wednesday, we hope we can recover. I hope we have not lost Giroud in the final minute. It's a stretched ankle. It doesn’t look good."
On the impact the Frenchman made after replacing Alexis, 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 take on Turkish side Besiktas on Tuesday knowing a win will be enough to take them through to the group stages of the Champions League, following a 0-0 draw in the first leg in Istanbul.