The 19-year-old suffered the injury during Saturday's 3-1 defeat at Hartlepool.
Newcastle boss Chris Hughton admits it's a chance the club take loaning out youngsters to lower league clubs.
Brighton boss Gus Poyet: "This is a major blow as Kaz has been in excellent form for us this season and at times he's been our matchwinner.
"We will liaise with Newcastle and their medical staff and I hope we see Kaz back in Albion colours before the season ends."