The Frenchman has struggled in recent weeks and his manager Manuel Pellegrini has confirmed that surgery was the recommended option to cure the problem.
"It's serious because maybe he will have surgery in the next days. I'm not a doctor but I think he will be out for around one month," Sky Sports News quotes Pellegrini as saying.
"He was training but he wasn't 100%. He didn't feel comfortable with what he was doing so the doctor decided that was the best option.
"Of course he's a very important player for us and it's not easy for us to play without Samir. But I never give excuses about players that, for different reasons, are not in our squad. We have an important squad."
Nasri has made over 100 appearances for City since joining the club from Arsenal in 2011.