Arbizu, who was preparing to lead the Pumas in Australia, injured his right knee in a practice game in the north-western city of Tucuman.
"I've already got it in my head that it's a problem of the cruciate ligaments and that I won't be at the World Cup," he said yesterday.
The 31-year-old centre, who was also injured during his country's second Test victory over France, has yet to undergo tests to confirm the extent of his injury.
Argentina coach Marcelo Loffreda is expected to name Martin Gaitan as Arbizu's replacement in his 30-man squad.
The Pumas will open the World Cup on 10 October when they take on hosts Australia in Sydney. They face Ireland on Sunday, October 26.
Meanwhile Wallaby great David Campese believes England have a good chance of winning the World Cup but he has warned Clive Woodward's men of the threat posed by New Zealand and Australia.
Campese, international rugby's leading try-scorer with 64 touch downs in 101 Test appearances, has turned 'Pommie-bashing' into an art form over the years with frequent criticism of England and their style of play.
But after predicting sound beatings for Martin Johnson's side during the summer tour Down Under, he was forced to back-track when England cruised to their first-ever victory on Australian soil having already accounted for New Zealand.
Now his stinging critiques of the Red Rose have been replaced by warm praise and although he believes England have the ability to lift the Webb Ellis Trophy on November 22, he feels the All Blacks are the team to beat.
"I think England's new style is great," he said.
"The nucleus of the team has been together for a long time, but their rugby has really developed over the last couple of years. It's important to have combinations which have been established for a while.
"They have played very well recently and are on a roll after the Six Nations. But they've had a bit of a a break since winning the Grand Slam and their summer tour, so now they have to start again that's something you've got to look at.