City have decided to send the England Under 21 international under the knife and City chief Sven Goran Eriksson expects Johnson to be out of action for up to a month.
"He's had his operation on his groin problem and if we are lucky we could have back after the international break but I'm not sure exactly," Eriksson told the club's official website. "He will be away for three or four weeks.
"It's a pity but we had to do something, because he started the season so well but over the last month he has had problems, being not able to train every second day.
"As a youngster he needs to train without pain so we had to do something, it's better this way."