Monreal failed to travel to Germany because of a back problem while Chambers has succumbed to tonsillitis and will be assessed again on Tuesday morning.
It potentially leaves Arsenal without three full-backs as Mathieu Debuchy, who was already suspended for the Group D opener, faces an extended spell on the sidelines because of an ankle problem.
Chambers had been earmarked to replace Debuchy but should he fail to recover, 19-year-old Spaniard Hector Bellerin will add to his solitary senior appearance for the Gunners.
Wenger is confident Bellerin can plug the gap at the BVB Stadium Dortmund. Kieran Gibbs will start at left-back in place of Monreal.
“In defence we are….the Debuchy injury has put us in a position where we don’t want more injuries,” Wenger said.
“We have Bellerin who I think is now ready to play. He’s a boy with personality who isn’t fazed by the pressure.
“That’s a very important quality when you’re a young boy playing at a big club. His transition game is fantastic. He’s very quick and his final ball is good as well.
“He lacks a bit of experience as a defender, but he’s very dangerous going forward.”
Attacking midfielder Shinji Kagawa is not an automatic starter for Dortmund, despite scoring and claiming an assist on his return to the German club on Saturday.
Boss Jurgen Klopp said: “For a first game back it was an extraordinary one for him on Saturday. We saw the opportunity and used it to bring him back and at least here everyone is happy.
“A decision whether he will play will be taken in the morning.”
Sven Bender, who missed the World Cup through injury, is fully fit after coming on as a substitute on Saturday and he could replace Serbian midfielder Milos Jojic.
Watch Borussia Dortmund v Arsenal live on Sky Sports 5 at 7.45pm on Tuesday.