Stones, 29, suffered a muscle injury in pre-season and missed City’s opening two Premier League matches and remained on the bench for their Super Cup win.
The next international break is between 4 and 12 September.
Stones could miss England’s Euro qualifier against Ukraine and a friendly against Scotland next month.
He is set to miss City’s next two Premier League games against Sheffield United on 27 August and Fulham on 2 September.
The club are also without key midfielder Kevin de Bruyne, who has had surgery on a hamstring injury and could be out of action for four months.
