A timeframe has not been placed on when the Ukraine international might return to action, with City announcing ahead of Tuesday's Champions League match against Atalanta that he "will be assessed over the coming days to determine the extent of the problem".
There will be fears Zinchenko is the latest City player to fall victim to a serious knee problem, with Leroy Sane and Aymeric Laporte currently recuperating after surgery during the opening weeks of this season.
Zinchenko's own opportunity to establish himself as a reliable option at left-back for Pep Guardiola came after Benjamin Mendy underwent knee operations in each of the past two seasons, while Ilkay Gundogan sat out the majority of 2016-17 with a ruptured cruciate ligament.
After impressing in Mendy's absence last term as City won an unprecedented domestic treble in England, Zinchenko was rewarded with a contract extension running until the end of the 2023-2024 campaign.
Mendy has returned to fitness, while Guardiola bolstered his options at left-back by re-signing City youth-team graduate Angelino from PSV during the close season.