The Championship club announced Smith, assistant head coach Craig Shakespeare and first team coach Liam Bramley have left the club following the poor run of form.
Norwich sporting director Stuart Webber said club felt the decision was necessary to boost hopes of an immediate return to the Premier League.
Dean Smith has been sacked at Norwich head coach following a poor run of form
Frustration had grown among Norwich fans following a downturn in the teams' form
'This was a tough decision, but one that we felt was necessary to give ourselves the best possible chance of achieving our objective of promotion to the Premier League this season,' Webber said.
'We would like to place on record our thanks to Dean, Craig and Liam, who have always put the best interests of the football club first.
'With just under half of the season remaining and three consecutive home games on the horizon we now have a real opportunity to build some forward and positive momentum, both on and off the pitch.'
Steve Weaver and Allan Russell have been placed in charge on an interim basis.
The Championship club has said it will seek to 'identify and appoint a new head coach that is able to deliver both the level of performances required to challenge at the top end of the league whilst implementing a consistent style of play.'
Norwich suffered a 2-1 defeat to Luton Town on Boxing Day despite the hosts having 10-men
Smith had been in charge at Carrow Road since November last year, when he signed a two-and-a-half year deal at the club, following the dismissal of Daniel Farke.
The former Aston Villa boss was unable to save the Canaries from relegation from the Premier League.
Smith, 51, had insisted following the club's relegation that Norwich would have a tilt at the Championship, having won the title the last two occasions they had been in the league.
An automatic promotion push has faltered despite a positive start to the campaign, with the club currently 12 points adrift of the top two in the Championship.
Norwich lie fifth in the Championship but have suffered seven defeats in their last 12 matches
Norwich currently lie fifth, but only occupy a playoff place on goal difference.
Smith's side suffered a 2-1 defeat to Luton on Boxing Day at Kenilworth Road, with the hosts scoring an 89th minute winner through Cauley Woodrow, despite being reduced to 10-men.
The result continued Norwich's poor run of form, having suffered seven defeats in their last 12 league matches.
Norwich are set to host Reading on December 30, before welcoming Watford to Carrow Road on January 2.