Giroud, 27, was hurt late in his side's 2-2 Premier League draw with Everton on Saturday, with media reports suggesting the France forward could be out for up to three months.
Wenger said he would definitely not play against Besiktas at the Emirates Stadium, with an assessment by a specialist the same day likely to shed light on how long he may be out.
"Olivier will not play against Besiktas and will see a specialist, then we'll make an announcement of how long he'll be out," Wenger told reporters on Tuesday.
"It can be (a long term injury). We'll see tomorrow. I don't know (if it's broken). It's sad for us but we are focused on the game."
The first leg finished 0-0.
Theo Walcott is still returning to full fitness after a long layoff and Wenger said he was yet to give thought as to whether he would delve into the transfer market should Giroud, who was hurt shortly after scoring Arsenal's 90th minute equaliser at Goodison Park, be a long-term absentee.
Midfielder Mikel Arteta is also out through injury, while Aaron Ramsey is suspended after being sent off in the first leg.
Victory over would see Arsenal reach the Champions League group stage for the 17th straight season, and Wenger said that experience was key after a tough first leg encounter.
"Experience plays a big part. We have big experience in the Champions League of playing high pressure games and we can use that," he said.
"This group is strong and mentally prepared and ready for the fight. What's most important is that we go out and play at our best."