As a result, Ki will not play in the club's remaining two Barclays Premier League matches, the club said on its website, adding that he had the surgery to allow him to return in time for the club's pre-season preparation.
An official at Ki's agent, C2Global, said it will take three to four weeks for the 26-year-old defensive midfielder to recover.
Ki scored eight goals this season, becoming the first Asian to score eight goals in a single season.
He was ranked third on the 50 Best Asian Players 2015 list released by the British football magazine FourFourTwo last week. Bayer Leverkusen's South Korean forward Son Heung-min topped the list, while FSV Mainz's Japanese attacker Shinji Okazaki placed second.