Sigurdsson suffered the problem during Everton's 2-0 home win over Brighton and Hove Albion last weekend – although he was still able to complete the full 90 minutes at Goodison Park.
The 28-year-old was sent for a consultation with a specialist after the victory, who confirmed he would be sidelined until at least late April.
However, Sigurdsson should recover in time to feature for Iceland at the upcoming FIFA World Cup in Russia.
"We'll continue to assess Gylfi's progress on a week-to-week basis and the medical team will work very closely with him, as they would with any injured player, to get him back playing as quickly as possible," Toffees boss Sam Allardyce said.
Sigurdsson has made 33 appearances in all competitions this season following a big-money move from Swansea City.