The France international had set up the first goal for Roberto Mancini's side but was forced off after colliding with Jonas Gutierrez
The France international collided with Jonas Gutierrez in the 36th minute before hobbling to the touchline towards the City bench. The 25-year-old was subsequently replaced by Aleksandar Kolarov.
Nasri had assisted Manchester City's opening goal after just 10 minutes as the midfielder received a fine pass from Yaya Toure before squaring the ball for Sergio Aguero to finish.
Roberto Mancini confirmed after the game that nasri is likely to miss next week's clash with struggling Reading, and hailed the Frenchman's performance during his time on the pitch.
The Italian told the club's official website: "We will see tomorrow, but I don't think that for [next] Saturday, he will be ready.
"He played very well, I always want him to play like today. If he plays, and he plays like today, we have less problems."