The Ajax striker damaged his ankle during the 0-0 first-leg draw in Reykjavik last Friday.
Sigthorsson had been receiving treatment in an attempt to remedy the problem, but it has now been confirmed that the 23-year-old will be unavailable for Tuesday's clash in Zagreb.
"From the beginning I was afraid I would miss out on this match, and it is very disappointing to miss the most important game in the Icelandic football history," Sigthorsson told Icelandic broadcaster RUV.
"But I will follow it with excitement and am sure that the guys will succeed. And I will be ready for Brazil next summer."
Veteran Club Brugge striker Eidur Gudjohnsen is expected to start in Sigthorsson's absence as Iceland attempt to qualify for a major tournament for the first time in their history.
And coach Lars Lagerback is confident they can overcome Croatia and clinch their place at next year's finals.
"I always try to find solutions to problems rather than lament over them," Lagerback said.
"We have nothing to lose and everything to gain in this game.
"We know Croatia are a team of exceptional quality and (Mario) Mandzukic is one of the most versatile strikers in the game but I have plenty of faith in my team's character."
