Neil, 35, helped the Canaries earn promotion to the Premier League after joining the club in January 2015, but they suffered relegation last season.
City had failed to win in five games under the former Hamilton boss, leaving them nine points outside the top six.
First-team coach Alan Irvine will take charge of the team for Saturday's game with relegation-threatened Blackburn.
A club statement said: "The board has taken the tough but unanimous decision, believing it is in the best interests of the club for a new manager to be in place through a crucial summer transfer window."
Norwich were second in October, but have won just seven of their last 24 Championship games and dropped to eighth.
They were thumped 5-1 at Sheffield Wednesday on Saturday - their 10th away defeat of the season - and drew 1-1 with lowly Bristol City on Tuesday in Neil's last game in charge.
Neil held his usual pre-match press conference on Friday, just hours before he was sacked, and told BBC Radio Norfolk that the Canaries had not lived up to expectations this season.
"There was an expectation for us, from the squad, from the management, from the fans, from everybody connected with the club, that we would have a better season than we've had," he said.
"All I can do is work as hard as I can to make it better. Sometimes you need to take a step back to take two or three steps forwards, and we are doing everything we can but there isn't a solution that's going to happen tonight and it's not going to happen next week.
"It's going to take a period of time and then things will improve." - BBC -