Mendy suffered the injury during the first half of the Premier League leaders' 5-0 victory at home to bottom side Crystal Palace last Saturday.
The Frenchman had been on impressive form since he joined City from Monaco for a reported 52 million pounds ($69.97 million) fee in July.
He joked on his Twitter feed that he would be joining "Injury FC" on loan for a couple of months but hoped to return stronger.
City said on their website (www.mancity.com) that the player had travelled to Barcelona to see a specialist, after initial tests in Manchester, with the results on Thursday confirming the extent of the injury.
"Benjamin will undergo surgery tomorrow in Barcelona, and everyone at the club wishes him a speedy recovery," added City, who travel to Chelsea for Saturday's clash between the reigning champions and current leaders.
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
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