City gave no timescale for the player's return, but British media reported that Mendy, who missed the majority of last season with a ruptured cruciate ligament in his right knee, would be sidelined for several weeks.
City said in a statement that Mendy, who played the full 90 minutes in their 3-1 win over rivals Manchester United on Sunday, had travelled to join up with the France squad before withdrawing.
"The 24-year-old defender attended Dr. Cugat’s clinic in Barcelona where scans revealed that surgery was required," the City statement said.
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"That surgery was conducted on Wednesday evening and everyone at Manchester City wishes Benjamin a speedy recovery."
City top the Premier League table with 32 points from 12 games, two points clear of Liverpool in second.
France play the Netherlands in a Nations League match on Friday, before playing Uruguay in a friendly four days later.
(Reporting by Toby Davis, editing by Pritha Sarkar)
