The France international suffered a partially ruptured knee ligament after a challenge with Mapou Yanga-Mbiwa at St James' Park.
The initial fear was that he may be ruled out long-term, possibly even for the rest of the domestic season and the World Cup.
But he is now expected to be back in action by mid-March, with the player himself breaking the news via social media.
"Thank you everyone for your kind words and overwhelming support, I suppose it's kind of good news that I will be out around 8 weeks," he wrote on Twitter.
Nasri looks set to miss a number of key Premier League matches, including the visit of Chelsea to the Etihad Stadium on 3 February and the home derby clash with Manchester United on 1 March.
He is also likely to sit out the first leg of City's Champions League last 16 tie with Barcelona on 18 February but could return for the second leg at Camp Nou on 12 March.
City boss Manuel Pellegrini was angered by Yanga-Mbiwa's tackle in the 75th minute and felt the player should have been sent off, rather than booked.
"It's very serious. It was a very unfair kick and the player of Newcastle, it was directly a red card. I don't understand why he was not sent off," said Pellegrini.
@diegtristan8 rags showing their true colours these days.- prawnsandwich