Sigthorsson opened the scoring in Ajax's 5-0 Eredivisie victory on Saturday, but had to be withdrawn shortly after a crude challenge from Willem's Ali Messaoud.
Coach Frank de Boer said after the game that the Icelander would likely be sidelined for two to three weeks.
And Ajax announced on Monday that Sigthorsson will be unavailable until after the mid-season break, meaning he misses Wednesday's UEFA Champions League fixture with APOEL and Eredivisie games against Utrecht, Vitesse and Excelsior.
A club statement read: "Kolbeinn Sigthorsson will not be in action for Ajax for the rest of the calendar year.
"The striker left Saturday's home match against Willem II with a hefty outer ankle bracelet on.
"It is now known that the recovery will take three to four weeks. Since Excelsior - Ajax on December 21 is the last game of this calendar year, Sigthorsson will only be able to play again in the second half of the season."
