A fuller assessment of how long Giroud will be out for should come after he has seen a specialist on Tuesday
He sustained the injury in Saturday's 2-2 draw with Everton.
"Olivier will not play against Besiktas and will see a specialist, then we'll make an announcement of how long he'll be out," Arsenal manager Arsene Wenger said.
The loss of Giroud, who struck the injury-time equaliser at Goodison, has robbed Arsenal of their first-choice striker.
Wenger may now be forced to dip into the transfer market in search of a replacement if the Gunners' worst fears are realised and the Frenchman faces an extended spell on the sidelines
"It can be (a long term injury)
We'll see tomorrow
I don't know (if it's broken)
It's sad for us," Wenger said
Summer signing Alexis Sanchez is likely to operate as the loan striker against Besiktas, although there are doubts about his ability to perform the role
Yaya Sanogo, Lukas Podolski or Joel Campbell could also start
Source : PA