The AC Milan forward will miss Wednesday's encounter after pulling up with a knee injury in training this week.
The AC Milan striker picked up a knee problem in training this week and Italy's football association (FIGC) confirmed he had departed the squad following the side's meeting with the head of the Catholic Church.
"Mario Balotelli will not play in the Italy-Argentina game," the FIGC said in a statement on its website.
"The Azzurri attacker, who yesterday had stopped during a light workout due to pain in his knee, has not recovered from his injury and gone back home.
"Balotelli left Rome after the audience at the Vatican with Pope Francis."
"He has a minor problem with his right knee, the one that he's undergone surgery on in the past and is occasionally a bit swollen," Castellacci told the official FIGC website.
"There's some fluid in his knee, but nothing to worry about it. He left the pitch for precautionary measures."