The Magpies midfielder was stretchered off in the first half of Newcastle United's defeat at Brighton on Saturday evening and scans have now determined the extent of the injury.
He will not require an operation and will begin a rehabilitation programme with the club's medical team to enable him to reach full fitness as soon as possible.
Hayden has played 27 times this term and recently made his 100th Premier League appearance for the club.
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."