The 20-year-old midfielder was first troubled by an ankle problem while on international duty last summer, and apart from a pre-season appearance in the Emirates Cup has not played a competitive match for the Gunners.
Wilshere, who needed surgery after initially wearing a protective boot, was set to return 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.
The fitness of the combative midfielder will also be of concern to England boss Fabio Capello as he prepares for his side's Euro 2012 campaign in Poland and Ukraine this summer.
Wenger, though, said: "I would not [worry] at the moment [about the summer].
"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.
"From day one, when you are completely fit to practice again, to be match fit you count at least six weeks."
Wenger added: "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]."
Arsenal suffered a third straight Premier League defeat when they lost 2-1 at home to Manchester United last Sunday, which left them five points behind fourth-placed Chelsea.
Wenger's decision to substitute livewire Alex Oxlade-Chamberlain - who actually had a slight calf problem - for the ineffectual Andrey Arshavin was greeted with chants of "you don't know what you are doing" from some sections of the Emirates Stadium.
While the Arsenal manager accepts everyone is entitled to vent their frustrations, Wenger is not about to take things personally as he prepares for Sunday's FA Cup fourth-round tie against Aston Villa.
"What is difficult to take is that all the three games we could have won," he said. "That makes me think that just a fraction of giving more will get us back on track and we will go on a run again.
"We are five points behind Chelsea and, at the moment, the title is out of sight, of course.
"I have a lot of regrets because I see Manchester City without Vincent Kompany and Yaya Toure - you suffer.
"We had 10 players out, and I do not think any team have dominated this championship this year.
"For us, at the moment we have to just try to come back closer to Chelsea."
