The centre back, who turns 34 this month, now faces a race against time to get back fit in time for the rest of the season, with the Gunners hoping to enjoy success in the Europa League and the final eight matches of the Premier League season.
A statement from the Arsenal medical staff read: "The procedure has been a success and David is now back at home rehabilitating.
"He will be able to return to daily support and recovery with our medical team at the training centre in the coming days.
"David is expected to be back to full fitness and available for selection in the upcoming weeks."
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