The 21-year-old midfielder is also a doubt for Sunday's Premier League trip to Old Trafford as well as England's forthcoming friendlies
The England star was ruled out of the 2-0 win over Liverpool after suffering a recurrence of his long-running ankle problems, which have now put paid to his hopes of facing Jurgen Klopp's side and could also see him miss Sunday's Premier League showdown with Manchester United, as well as England's upcoming friendly fixtures against Germany and Chile.
"Jack Wilshere has not travelled," Wenger told reporters on the eve of Arsenal's game at Signal Iduna Park. "He has another test on Thursday if he does not pass that he is out for Sunday and for England.
"Serge Gnabry has travelled and Kieran Gibbs has travelled too."
The Premier League leaders go into the game level on points with Dortmund but having lost 2-1 to the Bundesliga side at the Emirates Stadium a fortnight ago, and Wenger is looking forward to the return fixture.
"We are a positive side, Dortmund are a positive side so you have a guarantee both sides will try and win the game," he added.
"We lost the first game because we wanted to win it. We got caught on the counterattack because we were not happy with the draw."
Robert Lewandowski was the match-winner for Dortmund in north London and Wenger is well aware of the danger the Pole poses.
"Usually, at home, Lewandowski is quite dangerous," the Arsenal boss observed, "but the best way to keep him quiet is for us to have the ball."