The France left-back underwent surgery to repair a meniscus problem in his left knee last week.
It is a second major injury setback for the 24-year-old since he joined City in 2017 after missing the majority of last season with cruciate ligament damage in his right knee.
Asked if there was yet a timescale for Mendy's recovery, Guardiola said on Friday: "Ten to 12 weeks."
Mendy joins team-mates Kevin De Bruyne and Claudio Bravo on the long-term injury list while Bernardo Silva has been ruled out of the Premier League champions' trip to West Ham on Saturday with a knock.
There is also doubt over whether the Portugal international will be available for Tuesday's Champions League clash at Lyon.
Speaking at his pre-match press conference, Guardiola said of Silva: "He cannot play this weekend. The injury is not too big but I don't know if next Tuesday he will be available."
Guardiola this week reiterated his desire to manage in international football one day while speaking at an academic conference in Liverpool.
But the 47-year-old, who took charge at the Etihad Stadium in 2016, recently committed to City until 2021 and says he could yet extend his stay further before pursuing other ambitions.
The former Barcelona and Bayern Munich boss said: "I said many times that I extend the contract and I don't deny too if it is going well to stay more years here.
"Everybody has dreams and when I was a little boy I had dreams. Sometimes they are accomplished and sometimes not. I said maybe in the future I would like (international management).
"Maybe I will change my mind later but I am fully convinced in my mind here."
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