The France international was withdrawn after 29 minutes during Pep Guardiola's side's 5-0 win over Crystal Palace on Saturday.
Speaking before City's Champions League clash with Shakhtar Donetsk, Guardiola suggested that the 23-year-old might train later on Monday, but Mendy did not appear with the squad.
City's £52m summer signing from Monaco will travel to Barcelona to see specialist Roman Cugat, a close friend of Guardiola who also treated City pair Vincent Kompany and Kevin de Bruyne last season.