The former Canaries goalkeeper was appointed full time manager of the club following their relegation to League One in May, having held the role for a short period on a temporary basis prior to becoming full time boss.
The first league game of the season for Norwich resulted in a heavy 7-1 defeat for the club at home to Colchester, where Town striker Kevin Lisbie scored twice for his loan club, to condemn the Norfolk side to a rude awakening to life in League One.
Despite a 4-0 win against Yeovil in midweek in the first round of the Carling Cup, it was not enough to save Gunn's job, and assistant manager Ian Butterworth will now take charge of the clubs next game.
Confirming the news a statement from the board who appointed Gunn just two months ago said: "Bryan has worked tirelessly for this football club for more than two decades, not least since taking over team affairs back in January.
"However the board met this week following Saturday's unacceptable record home defeat in our opening league game of the season."