The 24-year-old has been ruled out of action for at least three weeks with a hamstring problem.
Gibbs was substituted after 53 minutes of Saturday’s 2-1 victory over Crystal Palace when he suffered the injury.
Nacho Monreal came on as a replacement against Palace and will almost certainly start in the Istanbul match.
Arsenal already have doubts over Laurent Koscielny for the Besiktas tie, while Germany international Per Mertesacker has just returned to training following the World Cup.
Looks like the new fitness trainer Wenger brought in over the summer is already well versed in Arsenal tradition.- fictionalemu