"After tomorrow he is travelling to Barcelona to see what he has," said City manager Pep Guardiola.
"The first impression is that it will be a little bit long, unfortunately longer than we expect," he added, declining to give details of the injury.
Premier League leaders City have used Spanish doctor Ramon Cugat to help with some injured players since Guardiola, the former Barcelona manager, joined the club last season.
Mendy, who has made an impressive start to his career at City following his move from Monaco, for a reported 52 million pounds ($69.97 million) fee, missed Tuesday's 2-0 win over Shakhtar Donetsk in the Champions League.
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"It is very frustrating for him first as a person, I feel sad for him, like I felt for Ilkay Gundogan," said Guardiola, referring to the German midfielder who missed most of last season with injury.
"For the way we want to play we will lose a lot, he is a unique player.
"We have alternatives in our squad, Danilo, Fabian Delph, Fernandinho, even (Ukrainian midfielder Oleksandr) Zinchenko," added the Spaniard.
(Reporting by Simon Evans, editing by Pritha Sarkar)
