The midfielder left the field on a stretcher during the first-half of the Magpies’ defeat at the Amex Stadium following a freak collision with Brighton and Hove Albion’s Yves Bissouma.
The club have confirmed the 26-year-old has suffered a “significant knee injury”, though it will not require surgery following further assessment.
On Saturday night, Hayden tweeted: "Gutted all round is an understatement! I will be doing my utmost to recover as quickly as I can from this injury to help the team."
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It leaves the Magpies without one of those most experienced players for a critical part of the campaign.
Battling to retain their Premier League status, Bruce’s side face Tottenham, Burnley, West Ham United, Liverpool, Arsenal, Leicester, Manchester City, Sheffield United and Fulham in their final nine games.