Mendy seemed in strong spirit despite the injury and tweeted he was joining Loan FC.
Following the procedure, Mendy posted a picture on Twitter, with the caption: 'Surgery done: Jese and I nailed it. See you asap guys'.
City have won five and drawn one of their first six league games this season - but today's game is undoubtedly the biggest test of Guardiola's new-look side.
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Given City's trip to Chelsea, questions may be asked why Aguero was in the Netherlands 48 hours before such a serious match.
City didn't give a likely timeframe for Mendy's absence. "I think days off are for players to be happy".
"I don't know right now [if City will sign someone]".
Before the injury, Mendy's ability to attack at pace along the flank, coupled with a risky delivery, had made City a more potent proposition than last term.
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However, the 23-year-old Frenchman suffered a nasty-looking knee injury during City's 5-0 win over Crystal Palace on the weekend and fans feared the worst as Mendy was immediately subbed off and soon seen trudging around in crutches.
Midfielder Fabian Delph deputised at left-back in the Champions League win over Shakhtar Donetsk, while full-back Danilo is another option.
City will now be without a recognised left back until January at the earliest.
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