Nasri picked up the injury in Manchester City's Champions League defeat to Real Madrid.
The Frenchman came off during the first half at the Santiago Bernabeu and is doubtful to face the Gunners in a top-of-the-table clash at the Etihad stadium, with both teams on eight points and two behind leaders Chelsea.
"I don't think he'll be ready for Sunday. We're going to try but it's going to be difficult," explained City manager Roberto Mancini.
Mancini has been boosted by the return of Argentine striker Sergio Aguero who could make his first appearance this season after overcoming a knee injury. Sapa-AFP