The 20-year-old was set to return from his ankle problem in early February, but felt pain when running in training earlier this week and will now have a series of consultations with specialists before deciding how to proceed.
But Wenger is not overly worried, and when asked about Euro 2012, he said: "I would not (worry) at the moment. We are now at the end of January. He has not played since summer, so for the friendly against Holland (on February 29) it is impossible."
He added: "From day one, when you are completely fit to practice again, to be match fit you count at least six weeks.
"Jack is gutted. It is a massive disappointment, but I am really disappointed for him as well because he is a football animal.
"I am so sad that at that age you have to be out for such a long time with not any obvious reason.
"If you had have told me that Jack would not have played one game by February, I would have said 'that is impossible'.
"We miss that little burst from Jack. Let's hope it goes well and we have good news (from the specialists)."