The Ajax forward has failed to shake off the ankle knock he sustained in Friday's 0-0 draw in Reykjavik, meaning Eidur Gudjohnsen is likely to deputise in Zagreb
The Ajax forward picked up an ankle knock during Friday's 0-0 draw in Reykjavik and, despite intensive treatment, has been forced to admit defeat in his battle to regain fitness in time 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 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."
Seasoned forward 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, with coach Lars Lagerback confident that the Nordic minnows can pull off a sensational upset.
"I always try to find solutions to problems rather than lament over them," the Swede 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."
Iceland's meeting with Croatia is set to kick off at 19:15 BST.