City staff have stayed in Germany to support the fan, who is being treated in hospital.
A 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.”
City won the first leg of the last-16 tie in Gelsenkirchen 3-2.