The 22-year-old Icelandic has had problems with his shoulder in the past and recently dislocated his left shoulder again.
After intensive investigation club and player decided for a rest period, but little progress was made in the this period.
Sigthorsson, who came over from AZ in 2011, already missed the majority of last season due to a fatigue fracture in his ankle.
He has only played nineteen of the 51 games he could have played for Ajax.
Frank de Boer does have limited options in club captain Siem de Jong and new recruit Ryan Babel who signed from Germany club Hoffenheim in August.
Ajax may look for cover in January with a long season only just beginning.