Barnett was charged after throwing the ball at referee Simon Hooper following his sending off in a Championship match against Portsmouth earlier this month.
The centre-half has already served a suspension for the initial red card, but will miss City's next two games.
The Canaries are set to turn Barnett's loan deal from West Brom into a permanent switch in January, but the former Luton player will sit out the Boxing Day trip to Crystal Palace and Tuesday's visit of Sheffield United.
Source: BBC Sport
Source: BBC Sport