Willett, 29, was due to partner Lee Westwood when the 72-hole tournament begins in Melbourne on 24 November.
But the Masters champion does not want to risk aggravating the issue that saw him miss October's British Masters.
"Considering everything, including the amount of travel involved and extra strain, I decided that it was not in my best interests," Willett said.
The four-day competition would have been the fifth tournament in consecutive weeks for Willett, who has dropped out of the world top 10 for the first time since his Masters victory in April.
Willett is second in the Race to Dubai and is tied for 54th in the penultimate tournament, the Nedbank Golf Challenge, after a round of 74 at Sun City.
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In March, the Gulf state said that those without papers would not be arrested if they left within 90 days.
The deadline was extended by another month, but so far only 60,000 out of an estimated 400,000 Ethiopians have left, the Ethiopian government says.
Ethiopians make up a large portion of the kingdom's undocumented workers.
All those without papers now face imprisonment or forced deportation.
Africa Live: Updates on this and other stories
Ethiopia's Communications Minister Negeri Lencho told the BBC he feared what could now happen to his compatriots who were still in Saudi Arabia, adding they must return "with a sense of urgency".
"They will be imprisoned and we don't want our citizens to face unnecessary imprisonment, or suffer any physical harm or humiliation," Mr Lencho said.
One of those who returned is 28-year-old domestic worker Nura Ahmed. "Life was really tough," she told the BBC's Emmanuel Igunza just after she arrived in the Ethiopian capital, Addis Ababa.
"Sometimes I was jobless because I did not have the proper documentation, so I had no freedom to move around.
"One can never be at peace there," she added.
In 2013, a number of Ethiopians died in clashes with Saudi police as they were being rounded up for deportation.
Saudi Arabia attracts migrant workers from around the world, particularly Africa, and south and south-east Asia.
Saudi authorities estimate that up to one million people are working in the country illegally.
So far, tens of thousands of people of different nationalities have taken advantage of the grace period and have either left or acquired correct papers.

The soap star earlier tweeted that the medication she was taking had stopped being manufactured.
A show source then confirmed that she would be "taking time off" from her role as Liz McDonald in the long-running ITV drama.
An ITV spokesperson said Ms Callard was set to return to work in May.
The actress confirmed to a fan on Twitter the latest update in her health battle.
She said that her medication had been pulled from production as it yielded "no profit", and added: "Saw a new Doctor today. Got hope! X".
Callard, 59, also told her followers: "Had a good day today, things are on the up! Thank you for being there!!!!! X"
She had tweeted earlier that she had "been battling the demons of depression" and thanked fans and fellow stars for their support.
The actress has been open about her struggles with mental health and in an interview with broadcaster Piers Morgan in 2014, said she had tried to take her life "maybe half a dozen times".
She said: "It wasn't a cry for help at all. I'd known for quite a while that I wasn't myself, but I didn't really know what to do about it."
Source: Mind
England's Danny Willett has withdrawn from the World Cup in Australia to avoid aggravating his back problem.
[NEXT_CONCEPT]
Ethiopia says that only a fraction of its citizens working illegally in Saudi Arabia have returned home before today's amnesty deadline.
[NEXT_CONCEPT]
Coronation Street actress Beverley Callard is set to return to the ITV soap next month after revealing she had "hope" in her battle with depression.