Nasri had already been ruled out of Saturday's Premier League trip to Hull City with a groin injury, but could now face a lengthy spell on the sidelines.
"Samir Nasri is serious because maybe he will have surgery in the next days," said Pellegrini. "I think he will be out for, I'm not a doctor, but around one month.
"He was training but he was not 100 per cent. He did not feel comfortable so the doctor decided that was the best option
"Of course he's a very important player for us. It's not easy for us not to play with Samir but once again I never give excuses about players that are not, for different reasons, in our squad."
Nasri has made six appearances in all competitions for City this season and is joined by Fernando (groin) and Stevan Jovetic (hamstring) in missing out on Saturday's match through injury.
Pellegrini's men will be looking for their first win in four Premier League matches on Saturday.
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