The French full-back has suffered a hamstring injury and will miss Sunday's trip to West Bromwich Albion.
Sagna will target London derbies against Crystal Palace and Chelsea at the end of October as potential return dates.
Sagna's injury will likely see Carl Jenkinson return to the starting XI.
Spanish winger Santi Cazorla is also out of contention for the West Brom game due to an ankle problem.
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- Norwich City