The England U21 star has been struggling with the injury for the last few weeks and was excused from the last U21 squad by coach Stuart Pearce to rest the problem.
But Johnson was forced off at half-time in last night's 1-0 win over Sunderland and City boss Sven-Goran Eriksson has confirmed the 19-year-old must go under the knife for the benefit of his career.
"One thing is clear, he cannot go on like this because he plays but then cannot train for a few days," he said.
"We all know what a talent he is, he should be getting better, but he is in pain one day and not on the next, so he's not taking that step forward. He would do if was fit."
Eriksson also confirmed that Nedum Onuoha will be out of contention for Sunday's trip to Portsmouth, although England star Micah Richards could return from the cartilage injury he suffered at Bolton last week.
"Nedum has a groin problem and he will be out for at least 10 days. There is no problem with Elano and Micah hopefully will play next weekend," added Sven.