The 24-year-old sustained the injury in City's Champions League win at Villarreal last week, and he was an unused substitute in the team's victory over QPR this past weekend.
Nasri joined up with the national team this week, but after undergoing tests on his knee, it was determined he was not fit to participate in the upcoming matches.
A statement from the French Football Federation (FFF) read: "Samir Nasri reported for France duty at Clairefontaine with a left patellar tendon injury.
"A clinical examination and additional tests confirmed the inflammation and, consequently, the inability of the player to be fully fit has meant he will not play in the two internationals against the United States and Belgium. Samir Nasri will now be allowed to return to his club."
France manager Laurent Blanc also has fitness concerns with midfielder Yohan Cabaye and winger Florent Malouda.