The French midfielder was substituted after 37 minutes of Saturday's 4-1 Premier League victory over Norwich City following a clash of heads with Alexander Tettey.
And, despite the 29-year-old training on Monday, manager Arsene Wenger has revealed that he will not feature for the visit of Jurgen Klopp's men.
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Wenger also claimed that the clash with last season's runners-up would not be the deciding factor in who wins Group F and insisted his side will go into the game without fear after an impressive start to the season.
"It is not a decider but it's an important one," he added. "It's an 80 per cent game."
"The feel-good factor is down to the quality of the spirit of the team, the solidarity of the players, and their desire to do well.
"We know we are a team that looks for being of course successful, for that you need a special hunger and I believe these players have a special hunger.
"What is important is that we go into the game and focus on our quality, on our performance. For me that is more important than focusing on Dortmund.
"[We want to] come out of the game tomorrow and feel that we have played at our best. If we do we will be difficult to handle for everybody."
And on the subject of his own German contingent, which includes record-signing Mesut Ozil, the French manager said: "Germans have a reputation for being 100 per cent professional and we have not been disappointed."
The loss of Flamini will come as an added blow to Arsenal, with Theo Walcott having been ruled out for a further three matches following a setback in his recovery from abdominal surgery.