The 21-year-old defender has endured a tough time with injury in breaking the same bone twice, most recently in October last year.
Moore-Taylor managed 27 appearances and two goals last season, with Exeter finishing 10th in the league table.
City revealed surgery took place on Tuesday, telling the club’s official website: “Jordan’s foot will be immobilised for six weeks, after which the rehabilitation process will begin.
“It is too soon at this stage to estimate a precise return date for the defender but he will be unavailable during the opening weeks of the season.
“Everyone at the club wishes Jordan well for his recovery period, and we look forward to seeing him back in a City shirt again as soon as possible.”