The Welsh international injured his hamstring in the Gunners' 2-0 victory over Bayern Munich on Tuesday evening.
Initally, it was suggested that the former Cardiff midfielder could be on the sidelines for a mininum of four weeks.
And Wenger has confirmed the 24-year-old won't be available for selection until after the next international break.
"He had a scan today but he’s out," Wenger said.
"I believe he will be out until after the next international break.
"With the [last] international break, the fact that he played against Andorra certainly cost Bale and him as well."