The injured duo are unlikely to face Jurgen Klopp's men as the Gunners look to make amends for the defeat to the German side at the Emirates Stadium two weeks ago
Wilshere rolled his left ankle during a training session on Thursday and subsequently missed Arsenal’s 2-0 victory over Liverpool on Saturday.
Gibbs, meanwhile, suffered a calf injury during the win over Brendan Rodgers’ side and is also expected to miss out.
|11/2||Arsenal are 11/2 with Paddy to keep a clean sheet v Dortmund|
Jurgen Klopp is looking forward to taking on Wenger again - a man he greatly admires, despite the two having different ideas on how football should be played.
"He is really something. I love him. He is Sir Arsene Wenger," Klopp said.
"I like [Arsenal's philosophy]. I love it but I cannot coach it because I am a different guy. It is not my sport.
"I don't linking winning 80 per cent [of possession]. Sorry, that is not enough for me. Fighting football, not serenity football, that is what I like."
Klopp, who signed a two-year contract extension at the end of October, which keeps him at the club until 2018, will return to the touchline for this match after completing a two-game ban.
He will hope striker Robert Lewandowski continues his hot streak, with the Pole netting a hat-trick - his fourth for the club - in a 6-1 home win over Stuttgart on Friday.
Lewandowski also scored a late winner in Dortmund's 2-1 victory over Arsenal last month.
Dortmund have never lost at home to an English side in the Champions League, winning four of seven previous matches.
They will be without club captain Sebastian Kehl (ankle), despite the midfielder returning to training, while Lukasz Piszczek (groin) and Ilkay Gundogan (back) will also miss out.
Arsenal are unbeaten in their last 14 away matches, with 12 of them being wins, and they have not lost in their last four visits to Germany in the Champions League.
Arsenal are competing in their 16th successive Champions League campaign and will be well-placed to reach the round of 16 if they can beat Dortmund.
But they will be without Theo Walcott (abdomen), Lukas Podolski (hamstring), Alex Oxlade-Chamberlain and Abou Diaby (both knee), while young winger Serge Gnabry is struggling with an ankle injury.