The 22-year-old was ruled out of England's 2-0 win over Ukraine in a Euro 2024 qualifier shortly before Sunday's game at Wembley.
Foden had surgery in London and it is not yet certain now long he will be out of action.
City confirmed he will miss the match against Liverpool at the Etihad next Saturday.
"Phil will now return to Manchester to begin rehabilitation," said a City statement.
"He will not be fit for this weekend's Premier League game at home to Liverpool and it is unclear at this stage how long he will be unavailable for."
City are fighting on three fronts, sitting eight points behind Premier League leaders Arsenal, albeit with a game in hand.
They have five league games next month, including a match at home to the Gunners on April 26.
City also face German giants Bayern Munich in their Champions League quarter-final first leg on April 11, and play second-tier side Sheffield United in the FA Cup semi-finals on April 22.