Gunners manager Arsene Wenger insists the problem is minor, but his participation against Anderlecht in Tuesday's Champions League tie at the Emirates Stadium is also in doubt.
"There is a slight problem with Wilshere
I don't think he'll be available against Burnley," Wenger said.
"It's very, very short term
He took a kick on his knee
I don't know if Tuesday will be too early or not
He's not training at the moment."
Wenger delivered a positive update on Olivier Giroud, who is expected to rejoin the squad for training in mid-November after making a rapid recovery from his fractured foot.
Giroud had initially been ruled until January and Wenger said: "Olivier is miles ahead of schedule.
"He's doing very well
He's three weeks ahead of schedule and he will join normal training after the international break
Of course it's a big boost."
England winger Theo Walcott has been sidelined since January with a serious knee problem, but Wenger will not rush him back against Burnley.
"Theo is not ready yet
He's been out for too long to start the game
If I can give him some competition I'm happy to do it," Wenger said.
"He's eager to play, but that is always the period when the patience of the player is tested.
"They feel ready and want to play
Usually they realise only much later they are not completely ready.
"I know Theo very well
He's an intelligent player so he knows as well he's not completely there yet."
Source : PA