Everton claimed a 2-0 win over the Seagulls on Sunday (AEDT) at Goodison Park, but it came at a cost for the Iceland international.
A statement on the club's website read: "Gylfi Sigurdsson will see a specialist this evening to determine a timeframe for recovery from the knee injury he sustained in Saturday's Premier League win over Brighton at Goodison.
"It is anticipated that the 28-year-old Icelandic international could be sidelined for several weeks but it will only be after consulting with the specialist that a definitive timeframe will be known."
Sigurdsson joined Everton from Swansea in August for a reported £40 million (A$71 million) fee with £5 million (A$9 million) in potential add-ons.
He has scored four goals and provided three assists in 27 Premier League appearances and will be hoping the injury does not impact his preparations for Iceland's maiden appearance at the FIFA World Cup this year.