The 19-year-old, who picked up the injury during the Gunners' pre-season tour of America, was originally expected to be out for a few weeks, but he said on his Twitter page that the ankle is not responding to treatment.
"The bone is not responding. I will have surgery on my right ankle on Monday," wrote Wilshere.
"Hopefully I will return to action around Christmas time. I am in good hands! Thanks for your support everyone!"
Arsenal host Bolton Wanderers in the Premier League on Saturday.