Releasing a statement on Thursday afternoon, City explained that they are now working in conjunction with Greater Manchester Police and German police to gather more information.
The statement read, "Manchester City are aware of an alleged assault after the match at the VELTINS-Arena in Germany last night.
"The club are working with Greater Manchester Police and German Police to ascertain more information. Club staff have remained in Germany to support the family of an injured City fan who is currently in a critical condition in hospital.
"Anyone with information that can help the Police should contact 101."
Despite trailing in the closing stages, City won the game 3-2 after late goals from Leroy Sane, against his former club, and Raheem Sterling. Nicolas Otamendi had been sent off for the Sky Blues midway through the second half as a result of picking up two yellow cards.