Flamini made his comeback from concussion at the weekend against Crystal Palace but limped off minutes into the game complaining of a groin injury.
The Gunners head into one of the most crucial stages of their season, as they face an incredibly difficult 13 days.
They then have to travel to Dortmund and Old Trafford in quick succession, and the loss of midfield general Flamini is a massive blow to Arsenal's chances.
Since returning on a free this season, the Frenchman has established himself as a vital cog in the Arsenal side that have stormed to the top of the table.
Many sniggered at the budget buy, but former AC Milan man Flamini has dismissed doubts with a string of commanding performances in the Gunners midfield.
Should Flamini miss the full three weeks as expected, he will also sit out of Arsenal's game with high-flying Southampton.
After a relatively easy start to the season, pundits are calling for Arsenal to be judged after the next few weeks, and Wenger would have wanted his influential midfielder to be fit for the vital games.
Arsenal will also be without Mikel Arteta tonight as he serves his suspension for a red card on Saturday.
It is expected the Spaniard will return to the squad for Arsenal's next fixture.