The 19-year-old left the pitch after just seven minutes during the Gunners' pre-season friendly against the New York Red Bulls in the Emirates Cup on Sunday.
However, Wilshire doesn't expect to be sidelined for long.
"Ankle scan just showed some inflammation. Hopefully settle down in a few days," he wrote on his Twitter page.
The North London club open their season away at St. James's Park on August 14.