The Chelsea right-back featured in his side’s late 2-1 victory over Liverpool on Saturday, but will miss England’s upcoming fixtures against Wales and Latvia.
The 29-year-old was taken off in the 21st minute of City’s Premier League win over Brentford on Sunday, confirming after the game he had felt discomfort in his hamstring.
Flick’s men have now suffered two successive defeats in all competitions following their 2-1 loss to Paris Saint-Germain in the Champions League on Wednesday