The England international was thought to be a doubt after suffering a recurrence of an ankle injury, but Wenger has since declared that Wilshere has not travelled with the Gunners' squad.
"Jack Wilshere has not travelled," Wenger told reporters.
"He has another test on Thursday. If he does not pass that he is out for Sunday and for England."
Wenger's side currently top Group F on goal difference, but were beaten 2-1 by BVB on October 22.