The Iceland international played the full 90 minutes of the 2-0 win over Brighton at Goodison Park on Saturday but it has emerged he may have damaged ligaments.
Sigurdsson is due to have the problem assessed on Monday evening but could be out for the rest of Everton's campaign, which would also throw into doubt his chances of featuring in Iceland's first World Cup in Russia this summer.
His brother, Olafur Mar Sigurdsson, has spoken to Icelandic media in which he claims the joint of the right knee is damaged.
"It is anticipated 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 time frame will be known," said a statement from Everton.
The £45million club-record signing endured a difficult start to his Toffees career having moved from Swansea in the summer, as his struggles were matched by the team's.
His fortunes have improved since Sam Allardyce replaced Ronald Koeman in late November, scoring five of his seven goals in 17 matches since then.