Polls suggest voters will give the Independence party its worst electoral showing since its 1987 score of 27 per cent.
A party needs five per cent of the vote to be represented in the 63-seat parliament, the Althingi.
About 228,000 people are eligible to vote. Polls open at 9am (09:00 GMT) and close at 10pm, with final results expected early on Sunday.
Iceland's reliance on the financial sector has had a devastating impact; thousands of people have lost their savings and their jobs.
Icelanders had enjoyed a standard of living envied by the rest of Europe, but since the onset of the crisis the state has had to take control of three major banks. The currency, the Icelandic krona, has plunged.
Sigurdardottir supports joining the European Union and adopting the euro.
She says EU membership would shelter the island nation from global economic turbulence.
"EU membership application is a priority issue for the Social Democrats," she said on Friday.
"It is necessary to achieve stability."
But the Left-Greens are opposed but agree that debate on the issue is needed.