France international Nasri was stretchered off late in City's 2-0 Premier League win at Newcastle United on Sunday following a high challenge from compatriot Mapou Yanga-Mbiwa.
It was initially feared the 26-year-old may be out for several months, with manager Manuel Pellegrini describing his injury as potentially "serious" following the game at St James' Park.
That led to concern that he could miss the remainder of the season, while also casting his participation in this year's FIFA World Cup in doubt.
However, Nasri revealed on Twitter on Monday that he will be back in action approximately two months with a "partial rupture oof the internal ligament", although that means he is unlikely to be fit for City's UEFA Champions League last-16 tie with Barcelona.
"Thank you everyone for your kind words and overwhelming support, I suppose its kind of good news that I will be out for around 8 weeks," he wrote.
