Hughton was relieved of his managerial duties and replaced by youth team coach Neil Adams after Norwich's 1-0 home defeat to fellow Premier League relegation candidates West Brom on Saturday.
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That loss left Norwich just five points above Fulham, who are third from bottom heading into next week's clash between the two, after winning just three games since the New Year.
Hughton, a former team-mate of Lineker's at Tottenham, was notified of his dismissal at Norwich's training session on Sunday and the England legend took to Twitter to question the timing of the 55-year-old's axing.
"Chris Hughton has been sacked by Norwich. Now? With five games to go? Utterly bonkers!" Lineker tweeted.
"Statistics show that the thinking, that a new man in charge brings an immediate upturn in fortunes is a complete myth."
Hughton arrived at Carrow Road in July 2012 after Paul Lambert departed for Aston Villa.
The Englishman guided the club to an 11th-placed finish in his first campaign in charge but found the going tough this season.
Norwich bosses finally pulled the pin after fans turned on the team in the aftermath of Saturday's loss.