The French global suffered the injury in Saturday's 5-0 Premier League victory over Crystal Palace at the Etihad Stadium.
Earlier, it was reported that City's star striker Sergio Aguero has suffered broken ribs after the accident in Amsterdam and it is likely that the Argentine will be out of action for some time now.
The 23-year-old French worldwide, signed for £50 million ($67 million) from Monaco in the summer, will undergo surgery in Barcelona on Friday on the injury he suffered in last weekend's victory over Crystal Palace.
Mendy travelled to Barcelona this week to see a specialist regarding his injury, and will now go under the knife on Friday - facing months on the sidelines.More news: Beyoncé lends her voice to help hurricane victims
He wrote, "Bad news guys".
Manager Pep Guardiola was pessimistic about Mendy's situation in the aftermath of the weekend's victory, suggesting the France worldwide could be unavailable for so long that City would have to pursue a replacement in the January transfer window. City's midweek match against Shakhtar Donetsk saw Fabian Delph fill in Mendy's position, and the only other suitable option ahead of the club's weekend encounter with Chelsea comes in the form of natural right back Danilo.
The Spaniard was asked whether he would consider looking for a replacement left-back in January and replied: "We will see in January".
Jonathan is ESPN FC's Manchester City correspondent.