Shaymaa Qasim Abdelrahman received the threat after she was made champion in Iraq's capital Baghdad on Saturday, according to media in Kuwait.
The 20-year-old, from Kirkuk, was said to have been left distressed by the phone call but insists threats will not stop her.
According to the Jerusalem Post, which cited Kuwaiti daily al-Watan, the student was told to join the caliphate or face being kidnapped.
But fresh from winning the contest - the first to be held in Iraq in more than 40 years - the beauty queen said she was determined to 'continue forward despite any obstacles'.
And she told NBC News: 'I want to prove that the Iraqi woman has her own existence in society, she has her rights like men. I am afraid of nothing, because I am confident that what I am doing is not wrong.'
In September, it was reported that organizers of the event were facing an angry backlash from religious hardliners and conservative tribal leaders who said such pageants are un-Islamic and threatened public morality.
Reuters said at least two young women had pulled out of the contest after receiving death threats.
And organizers dropped the swimsuit section of the competition and postponed the televised finale in an attempt to deflect some of the criticism.
But contestants backed by many ordinary Iraqis, remained determined to press ahead with an event they saw as marking a step towards normality in a society still deeply divided and traumatized 12 years after the U.S.-led overthrow of Saddam Hussein.
The first and last time Iraq participated in a major international beauty pageant was in 1972 when Wijdan Burhan al-Deen represented the country at the Miss Universe contest.
Qasim told AFP after her victory: 'I'm very happy to see Iraq going forward. This event was huge and put a smile on the faces of the Iraqis.'
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