The Gunners boss says the midfielder will be out until at least the end of January with an injury that was initially only thought to keep him sidelined for a matter of weeks
The England international underwent surgery on his ankle and is likely to be out until at least the end of January or early February, and Wenger says that the rest of his midfield will have to pick up the slack.
"The news we have is very positive but of course the time he will be out will be quite long," Wenger told reporters. "And it's very difficult to predict how long he will be out but at least four months for certain.
"I don't know what kind of impact it has," he said. "It makes us a bit short in midfield and it puts more pressure on our midfielders to perform game in, game out, because of less rotation possibility.
"But every club can be tested on that front so that shouldn't impact our end result of the season and shouldn't be any excuse at all.
"[Wilshere] can come back as well and be very strong and help us to finish well this season."
Wenger was asked what had been the cause of the injury, but admitted he did not quite know whether it was an old injury that had resurfaced or a new injury altogether.
"Basically what I've been told is we had to go in quite quickly to repair it and that's why we decided to do it so quickly.
"He had an early fracture at the age of 16 that healed and around that it created another opening.
"Is it down to a kick? Is it down to playing too much? I don't know, I'm not a specialist.
"[The injury] hasn't been changed because the fracture he had...didn't heal.
"But that's unfortunately what happened. He told me he felt that the first time against Switzerland [in England's Euro 2012 qualifier in June]. "
The manager also stated that winger Theo Walcott has a good chance of returning to action against their rivals Tottenham on Sunday.