The England international sustained an ankle injury in the 2-1 defeat to Manchester United that could sideline him until March
The England international limped off during the Gunners' 2-1 defeat to Manchester United at the weekend following a late challenge from Paddy McNair on the edge of the box.
Wilshere subsequently missed Arsenal's 2-0 win over Borussia Dortmund on Wednesday, with manager Arsene Wenger revealing after the match that he expected the midfielder to miss "the next few games".
However, it has now been confirmed that Wilshere will instead be sidelined until at least February, though the Gunners revealed that his operation had been a success.
Wilshere took to Instagram to confirm the news and said that "everything went well", while urging his fans to stay positive.
"Work hard for what you want because it won't come to you without a fight," he wrote. "You have to be strong and courageous and know that you can do anything you put your mind to.
"If somebody puts you down or criticises you, just keep on believing in yourself and turn it into something positive."