The French international suffered the injury in Saturday’s 5-0 Premier League victory over Crystal Palace at the Etihad Stadium.
The 23-year-old was signed for £52 million in the off-season from Monaco, but his City career has been interrupted as he faces several months on the sidelines.
"It is really frustrating for him, first as a person, but like what happened with Ilkay Gundogan last year, I am sad for him," manager Pep Guardiola said following his team's Champions League victory over Shakhtar Donetsk on Tuesday.
"We will lose a lot. He is a unique player - the joy he gives inside and outside the pitch. It is a major setback."
Despite the diagnosis, Mendy was able to keep his sense of humour on Twitter, saying he is "joining Injury FC on loan for a couple months."
Bad news guys ll be joining Injury FC on loan for a couple monthes with ruptured ACL... but will be back soon & stronger hopefully— Benjamin Mendy (@benmendy23) September 28, 2017
Mendy has made five appearances in all competitions for City in 2017-18, providing one assist.