Suicide bombers and insurgency in the country has also uprooted a further 1.9 million people who remain in Iraq yet have had to leave their homes.
"The Middle East is on the verge of a new humanitarian crisis unless the EU, US and other states take urgent and concrete measures," the London-based charity warned.
Speaking at the beginning of a two-day summit in Geneva held by the UN refugee agency (UNHCR), the human rights group called for more help to be given to Jordan and Syria who have taken the vast majority of refugees.
Figures from UNHCR show that, aside from Jordan and Syria, Egypt and Lebanon are also key players in assisting the Iraqi refugees, providing a home for 120,000 and 20,000 people respectively.
"AI is calling on the international community, in particular the US, EU and other states that have the capacity to do so, to share the responsibility by resettling Iraqis from Jordan and Syria, giving priority to the most vulnerable cases," a statement from the charity read.
It is thought that the US will accept around 7,000 Iraqi immigrants this year, a massive rise from 2006's number of 202.
However AI has called for structures to be put in place to manage the "humanitarian crisis".
"Such resettlement programs should go far beyond token numbers and should constitute a significant part of the solution to the current crisis."
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