Wilshere was unable to train on Tuesday and he did not fly out with the rest of the Arsenal squad to Germany for the Group F clash.
Wilshere, whose last appearance for Arsenal was as a 69th minute substitute in the 2-0 away victory over Crystal Palace, is understood to be suffering from a problem with his left ankle that he picked up last week.
Arsenal manager Arsene Wenger said: "Jack Wilshere has not travelled. He has another test on Thursday. If he does not pass that he is out for Sunday and for England."
Theo Walcott also missed the session despite widespread reports that he has stepped up his recovery in the last couple of days and could be available for Arsenal's Super Sunday clash with Manchester United.
However, defender Kieran Gibbs has given Wenger a timely boost ahead of the game, after taking a full part in Tuesday morning's training session.
Gibbs sustained a calf injury in Saturday's 2-0 victory over Liverpool, forcing him to be replaced by Belgium international Thomas Vermaelen after 76 minutes.
Robert Lewandowski scored a late volley to earn Jurgen Klopp's side a 2-1 win at the Emirates a fortnight ago, a result that ended the Gunners' perfect start and threw open Group F.
Group F is finely poised with Arsenal, Borussia Dortmund and Napoli all locked on six points at the halfway stage of qualifying.
And Gunners defender Per Mertesacker feels his side must stay relaxed against last season's beaten finalists.
Mertesacker said: "It is difficult to play Dortmund, especially away from home, but we have to keep our confidence. We are on a high level. We are top of the (Premier) League.
"We try to gain confidence and we need to get a good result over there.
"But we are relaxed. We did show already in the Premier League that we are one of the best teams.
"It is a little bit different in the Champions League, though, and we need a result there to stay (in line for qualification)."
Dortmund have never lost against English opposition at the Westfalenstadion, but Arsenal were within two minutes of winning there in September 2011 before the hosts scored a late equaliser.
Arsenal are also unbeaten from four away ties in Germany - the last being a famous 2-0 victory over the eventual European champions Bayern Munich in March.
Mertesacker said: "It is hard to describe what we will expect in Dortmund. Two years ago it was a tough game and some of us will remember that we were happy with one point."
Watch Dortmund v Arsenal live on Sky Sports 1 from 6pm on Wednesday.