The 21-year-old was substituted off in the 58th minute for Santi Cazorla during Arsenal's 2-1 defeat to Borussia Dortmund in the Champions League on Tuesday evening after aggravating his right ankle in the first half.
Wilshere required ice treatment after being replaced but the England international insists he is likely to be available for his side's trip to Crystal Palace on Saturday.
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"My ankle stopped and my body went over it and I jarred it a little bit.
"For five or 10 minutes it was painful, then I ran it off, but it made sense to put ice on it.
"I've done that before, even before I had surgery. It is just one of those things.
"Obviously I will have treatment tomorrow because it is still a bit swollen, but I should be all right for the weekend."
"I have done it before and it's painful for the first minutes or so, then you can run it off and I'm alright at the minute."
Arsene Wenger admits he is concerned over Wilshere's ankle problems and claims the midfielder was "handicapped" for the majority of his time on the pitch against Dortmund.
"You could see he was not completely himself and that's why I decided to take him off," Wenger told reporters.
"I think at the moment it's his desire to play, absolutely, but you could see tonight he was handicapped after the first tackle of the game. He landed awkwardly and he looked to me that he was limping a little bit.
"I'll see how he responds in the next two or three days but I will have to wait for the medical assessment."