The 19-year-old England international has been troubled by a stress fracture, but it was hoped the problem would heal itself with the help of a protective boot.
However, Arsenal have confirmed in a statement that Wilshere's ankle has failed to respond to the treatment and he will now go under the knife on Monday morning.
The midfielder is expected to be sidelined for several months.
"Throughout Jack's injury, the club has been guided by the continuous advice of several world-renowned specialists," said a club statement.
"The information attained this week has led to the conclusion that surgery is now required to gain an optimal response.
"Wilshere is now expected to be out for a period of months. Following surgery these timescales will become more specific."
A club spokesman added: "We have given Jack time to heal naturally which is important wherever possible with a young player.
"The latest scans show surgery is needed. Everyone at the club wishes Jack a speedy recovery."
Wilshere has been troubled by his ankle throughout the summer, having sustained the original problem in the Euro 2012 qualifier between England and Switzerland in June and then aggravating it in a pre-season game a month later.
And while it had been hoped Wilshere would return in a matter of weeks, manager Arsene Wenger is now expected to be without the player until the end of this year.
Wilshere wrote on his twitter account on Friday night: "Been in a boot for a month and the bone is not responding. i will have surgery on my right ankle on monday with the two best surgeons around.
"Hopefully i will return to action around christmas time. i am in good hands! thanks for your support everyone!"
The news also comes as a blow to England manager Fabio Capello, with Wilshere set to miss their final Group G qualifier against Montenegro on October 7.