The Wales midfielder has not travelled with the rest of the squad to Germany after suffering an ankle problem in training.
Ramsey's setback leaves Gunners boss Arsene Wenger short of options in midfield with Jack Wilshere and Abou Diaby also the sidelines with ailments of their own.
Tomas Rosicky has also been left out of the 18-man party as he is struggling with a knee injury, but new signings Mikel Arteta, Per Mertesacker, Yossi Benayoun, Andre Santos and Park Chu-young are available.
"I think Aaron Ramsey has been very influential in our team since the start of the season, but it is a good opportunity that we now have a big squad and that we can cope with it," Wenger told Sky Sports News.
"We have of course three midfielders out - Diaby, Wilshere and Ramsey - and it's many but we still hopefully have a strong midfield tomorrow [Tuesday]."