The England midfielder missed Saturday's 2-0 win over Liverpool after going over on his left ankle in training.
He had treatment yesterday and a final decision will be made today, but his prospects of going to Germany for Wednesday's vital group match look bleak.
The new injury is another blow for Wilshere, who has had persistent problems with his ankles.
Ironically, he also missed the Gunners’ last trip to Germany with a similar issue to his current problems with his left leg.
The ankle became inflamed before the game in March at Bayern Munich, which Arsenal won 2-0.
He was sidelined for six weeks.